Egg Matzah-Matzah Ashira

A. Understanding the liquids that turn flour into Chametz:
Water and water derivatives:[1] The Biblical definition of Chameitz refers only to dough that has been kneaded with water or with water derivatives. Only water or water derivatives can leaven the grain or flour.
Fruit juice-Does fruit juice turn flour into Chametz?[2] Dough that is kneaded with fruit juice [or other liquids defined as fruit juice] cannot become Chametz and [from the letter of the law] is permitted to eat on Pesach. This applies even if the dough remains the entire day without being worked on and rises. [The Ashkenazi custom however is not to eat such Matzah over Pesach, as will be explained in E.]
Mixture of water and fruit juice:[3] The above law that fruit juice does not leaven flour only applies if absolutely no water is mixed into the fruit juice. If however even a minute amount of water mixed into the fruit juice, then this water causes the flour to become complete Chametz of which one is liable for Kareis. Furthermore, this mixture of fruit juice and even a minute amount of water causes the dough to become Chameitz in even less time than plain water, in even less than Shiur Mil [i.e. 18/24 minutes].[4] Furthermore, it can become Chametz even if one works on the dough after the kneading.[5]

B. Matzah Ashira-Matzah kneaded with liquids defined as fruit juice [i.e. Egg Matzah]:[6]
Any dough which is kneaded with a liquid that is defined as fruit juice is considered Matzah Ashira. As explained above, dough that is mixed with 100% fruit juice cannot become Chametz, while dough that is mixed with water and fruit juice can become Chametz instantly, in even less than 18/24 minutes, and even while being worked on after the kneading. Thus, foods which are made of five grain flours and 100% fruit juice are not Chametz and, from the letter of the law, may be eaten on Pesach. Furthermore, even foods that are made of five grain flour and a mixture of fruit juice and water is not Chametz if it was baked immediately and did not wait at all prior to baking. Nevertheless, it is forbidden to initially bake Matzah with a mixture of fruit juice and water, lest one not be careful to bake it immediately.[7] Furthermore, the custom of Ashkenazi Jewry is to be stringent and not to make or eat Matzah Ashira of even 100% fruit juice throughout Pesach.[8] This applies even if the Matzah was baked immediately after the kneading.[9] One may not swerve from this custom.[10] [Thus, Ashkenazim may not eat egg Matzah or any Pesach product that states “Matzah Ashira” on them, and therefore, foods with the blessing of Mezonos is not available for Ashkenazim over Pesach. Such foods however may be eaten by Sefaradim, under a reliable Hashgacha, as they never accepted the custom to avoid Matzah Ashira which is made from 100% fruit juice.[11] However, there do exist Sefaradi communities that are stringent just like the Ashkenazim.[12] ]
Old or sick person:[13] An old or sick person [who cannot eat other Matzah or foods], may be lenient to eat Matzah Ashira during Pesach. [This refers to Matzah kneaded with 100% fruit juice. It is however forbidden for even a sick or old person to eat Matzah that was kneaded with a mixture of fruit juice and water.[14]]
Owning Matzah Ashira over Pesach:[15] It is permitted even for Ashkenazim to own Matzah Ashira products during Pesach, as the above adherence is only with regards to eating it, and not regarding owning.
Using Matzah Ashira for the night of the Seder:[16] [According to all opinions] one does not fulfill the obligation of eating Matzah with eating Matzah Ashira.[17] This applies whether during the [seder of the] first night [on the 15th] or the [seder of the] second night in the Diaspora [on the 16th].

Summary:
It is forbidden for Ashkenazim to eat Matzah Ashira throughout Pesach. It is thus forbidden for Ashkenazim to eat egg Matzah or any other Matzah which contains any liquid other than water. However, an old or sick person who cannot eat other Matzah or foods, may be lenient. It is permitted even for Ashkenazim to own such Matzah over Pesach. According to all, one cannot fulfill his obligation of Matzah on the first night of Pesach using Matzah Ashira.

Q&A

At what time must Ashkenazim stop eating Matzah Ashira [egg Matzah]?
Some Poskim[18] rule that even according to Ashkenazim one may eat Matzah Ashira [egg Matzah] until midday. However, practically, the custom is to avoid eating Matzah Ashira beginning from the time that one must stop eating Chametz, which is the beginning of the 5th hour.[19]

May one eat egg Matzah or other forms of Matzah Ashira?
It is thus forbidden for Ashkenazim to eat egg Matzah or any other Matzah which contains any liquid other than water. However, an old or sick person who cannot eat other Matzah or foods, may be lenient.

May one eat “Papouchado” cookies?
Based on the above, it is forbidden for an Ashkenazi to eat the “Papouchado” company Mezonos cookies which is made using fruit juice. The same would apply for any Mezonos cookies that is made using fruit juice, that it is forbidden for Ashkenazim to eat it. Many leading Sefaradi Rabbis forbid the eating of such cookies for any person, as they claim it is not possible to supervise in such companies that not even one drop of water mix within the fruit juice that is used. Furthermore, it was discovered that in such cookies there is water placed in the wine, and other chemicals and spices, and hence they rule that the above cookies are absolute Chametz, and may not be eaten even after Chametz if they were not included in the Mechiras Chametz. 

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[1] Admur 462/1 and 466/1

[2] Admur 462/1; Michaber 462/1; Rambam 5/2; Rif 10; Pesachim 35a

Other opinions: There is an opinion who rules that from the letter of the law fruit juice makes flour into Chametz. [Raavad 5/2; Rashi Pesachim 36a; opinion brought in Admur 462/7] Furthermore, they hold that it causes dough to become Chametz even quicker than water, [in even less than 18/24 minutes]. In their opinion, dough kneaded with 100% fruit juice has the same status as dough that was kneaded with a mixture of fruit juice and water, [of which even the dissenting opinion agrees it can become Chametz instantly]. Nevertheless, even according to this opinion, this dough is not considered Chametz Gamur but rather Chametz Nuksha, and is thus only Rabbinically forbidden. [Admur ibid; Peri Chadash 462/1; Raavad and Rashi ibid] Practically, the main Halachic opinion is like the lenient opinion, and thus from the letter of the law it is permitted to eat bread made of 100% fruit juice even if it was baked after 18/24 minutes. Nevertheless, the Ashkenazi custom is not to eat any Matzah made of fruit juice [Admur 462/7; Rama 462/4; Drashos Maharil Shabbos Hagadol p. 57] due to suspicion that perhaps a drop of water became mixed. One may not swerve from this custom, as we suspect for the above opinions that even 100% fruit juice makes dough into Chametz instantly. [Admur ibid]

[3] Admur 462/3 and 466/3; Michaber 462/2; Rambam 5/2 based on Pesachim ibid

Other opinions: Some Poskim rule that Chametz of water and fruit juice is Chametz Nuksha and is not Biblically forbidden. [Rabbeinu Tam, brought in Beis Yosef 462; See Kaf Hachaim 462/18]

Baking dough that was kneaded with fruit juice and water: See 462/3 and 466/1!

The law if liquids defined as fruit juice fell on Pesach flour and then dried out: See 466/1!

[4] Pure water does not cause dough that was kneaded with it to become Chametz unless it remains Shiur Mil without being worked on. However dough that was kneaded with fruit juice and water is hastened to become Chametz even if it does not remain a Shiur Mil without being worked on. [Admur ibid]  

[5] Admur 462/3; Michaber 462/2; Pesachim 36a; Kaf Hachaim 462/21

[6] Admur 462/3; Rama 462/4

[7] Admur 462/3; Michaber 462/2; Pesachim 36a

[8] Admur 462/7 “All the above is from the letter of the law, however in these provinces the custom is not to knead even with only fruit juice, and if one transgressed and kneaded it with 100% fruit juice, it is not eaten on Pesach even if it was baked immediately.”; Rama 462/4 “In these provinces the custom is not to knead with fruit juice”; Drashos Maharil Shabbos Hagadol p. 57

The reason: As we suspect perhaps a drop of water became mixed into the dough, and even a slight delay in the baking can render it Chametz. [Admur ibid; Drashos Maharil ibid; Levush 461/5; Gr”a 461] One may not swerve from this custom, as there are opinions [Raavad 5/2; Rashi Pesachim 36a; opinion brought in Admur 462/7] who rule that from the letter of the law [even 100%] fruit juice makes flour into Rabbinical Chametz even quicker than water, [in even less than 18/24 minutes], and has the same status as dough that was kneaded with a mixture of fruit juice and water, [of which even the dissenting opinion agrees it can become Chametz instantly]. [Admur ibid; Maharil ibid; Gr”a ibid brings both reasons as does Admur; P”M 462 A”A 4 “There are many reasons, although the main reason is to suspect for the opinion of Rashi”; Thus, in total there are two reasons why we do not eat Matzah Ashira over Pesach: 1) Perhaps it got water mixed inside and was not baked immediately and is hence Chametz. 2) Perhaps we rule like Rashi that Matzah Ashira is Rabbinical Chametz if it was not baked immediately.] Alternatively, another reason mentioned, is because one may come to eat Matzah Ashira on the night of the Seder and not be Yotzei the Mitzvah. [Levush ibid; Kaf Hachaim 462/40

[9] Admur ibid; Olas Shabbos 462/7; Chayeh Adam 126/7; M”B 462/18

The reason: Even if one transgressed and kneaded it with 100% fruit juice and baked it immediately, it is not eaten on Pesach, as we suspect that if we allow him to eat it, perhaps in another occurrence he will not bake it immediately, as the thought that perhaps some water got mixed in will not occur to him. [Admur ibid]

[10] Admur ibid; Mahariz Zayin, brought in Birkeiy Yosef 462/8; Kaf Hachaim 462/42

[11] Rav Avraham Azulaiy; Shaareiy Yeshua 6/4; Nechpa Bakesef p. 176; Birkeiy Yosef 462/7; Kaf Hachaim 462/41

[12] Kaf Hachaim ibid

[13] Admur ibid; Rama ibid

[14] Elya Raba 461/4; Kaf Hachaim 461/48

[15] See Admur 462/7 “One does not eat it on Pesach” and Admur 462/3 “If he transgressed and kneaded it with fruit juice and water and did not bake it immediately, it is forbidden to be eaten, but may be owned, so long as it did not stay a Shiur Mil without being worked on”

[16] Admur 462/1 and 6; 444/2; 454/4; 471/4; Michaber 462/1; Pesachim 36a

[17] The reason: As the Torah says to eat “Lechem Oini” which is poor man’s bread and not Matza Ashira, which “rich man’s bread”. Furthermore, one can only fulfill his obligation with Matzah that will become Chametz if it were not guarded against becoming Chametz, [and flour that is mixed with 100% fruit juice cannot become Chametz, as explained next]. [Admur ibid]

[18] Noda Beyehuda 21 brought in Kaf Hachaim 443/7

[19] Piskeiy Teshuvos 444/3 [He makes no mention of the opinion of the Nodah Beyehuda ibid]