What is the law if one cut onions with a dairy knife and cooked them in a meat pot together with water or other foods?
If one did not fry the onion first, but initially cooked the onions together with other foods in the meat pot [i.e. in a soup or Chulent], then if that food contains 60x versus the onion, or 60x versus the blade of the dairy knife, then everything is permitted, including the onion. This applies even if one cooked the onion in chicken soup, or a meat cholent. If, however, the food does not contain 60x the onion, or the blade of the knife, then if the pot or spatula was Ben Yomo of meat use, or there were meat ingredients in the pot together with the onion, then everything is forbidden [i.e. the pot, soup, and spatula]. If, however, there were only Pareve ingredients cooking in soup, and the pot and spatula was not Ben Yomo, then if the onion is a minority ingredient of the mixture, then the food remains permitted [and becomes dairy], although the pot is forbidden and must be Koshered. If the onion is the majority ingredient in the food, then everything is forbidden, even if the pot was not Ben Yomo. If one first fried the onion in a meat pot and then mixed it with other foods [whether Pareve or meaty/dairy], then in all cases, the other foods must have 60x versus all the onions, otherwise everything is forbidden.
Fried: If one fried onions that were cut with a dairy knife [that was used in the past to cut hot dairy] in a meat pot, everything is forbidden [the pot, onions and spatula].
Cooked with other foods: If one cooked onions that were cut with a dairy knife [that was used in the past to cut hot dairy] in a meat pot together with other foods, everything is forbidden [the pot, onions and spatula], unless the food contains 60x versus the blade of the knife [or onions, whatever is less], or the food is Pareve, and the pot is not Ben Yomo, and the onions are a minority ingredient, in which case only the pot is forbidden while the food remains Kosher.
A word of advice regarding Charif:
Due to the complex Halachic issues that a Charif vegetable poses if it is cut with a meat or dairy knife [and then gets used with the opposite food or vessel], it is highly recommended that every kitchen establishes a rule that all Charif vegetables be cut with a Pareve knife and Pareve cutting board. Experience has shown that leaving a meat or dairy cut Charif vegetable around the fridge is bound to create problems, as people forget its status and can come to use it for the opposite food.
 When measuring versus the onion, does one measure versus the entire onion or only a Netila worth of the onion? If the Charif food was sliced in half then one only requires 60x versus the Netila/finger area of the Charif food [i.e. 2 cm of each side of the slice ], or 60x versus the blade of the knife, whichever is less. [Michaber 96:1; Rama ibid that Bedieved we are lenient like Michaber; Peri Toar 96; Raavad Avoda Zara 76a, brought in Rashba ibid; Semag Lavin 140; Reah in Bedek Habayis 4:1, brought in Ran Chulin 41a; See Beis Yosef 96:1] If, however, the spicy food was cut into small pieces [less than a Netila worth-2 cm-each ] then according to all opinions if one went ahead and cooked it with the opposite food, one requires 60x versus the entire spicy food or 60x versus the blade of the knife, if it is of smaller size. [Rama ibid; Shach 96:9; Kneses Hagedola 96:34; Peri Chadash 96:8; Kreisi 96:6; Lechem Hapanim 96:10; Beis Lechem Yehuda 96:8; Chochmas Adam 49:3; Kaf Hachaim 96:22]
 Does one measure against the blade or the onion? If one cut a sharp food with a meat knife and cooked it together with milk, one needs to measure 60x in the dairy food versus the Netila area of the food, or versus the knife which he used to cut with. One can choose to measure against whichever amount is less; if the area of the blade is less than the Netila area, he may measure versus the blade; if the Netila area of the food is less than the blade one may measure versus the Netila. [Michaber 96:1; This applies even according to the Rama as the food has absorbed Heter and not become Chanan.; Taz 96:6; Shach 96:9; Lechem Hapanim 96:9; Beis Lechem Yehuda 96:7; Chavas Daas 96:5 Biurim 1; P”M 96 M.Z. 6; Kaf Hachaim 96:21]
How much of the blade is one to measure against? If one is unsure how much of the blade was used to cut with, one is to measure 60x against the entire blade. [Shach 96:8 Taz 96:4; Rashal Gid Hanashe 42; Kol Habasar 62; Kneses Hagedola 96:33; Minchas Yaakov 61:7; Lechem Hapanim 96:7; Beis Lechem Yehuda 96:5; Chavas Daas 96:4; Chochmas Adam 49:2; Kaf Hachaim 96:17]
Measuring versus the amount of dairy the knife absorbed: In all cases that one is aware of the amount of hot dairy that the knife was used for cutting since its purchase, then one may measure versus the meat if it is a smaller amount than the blade or food. [Bach 96; Zivcheiy Tzedek 96:19; Kaf Hachaim 96:124]
 Taz 96:5; Shach 94:23; Maharam Melublin 28; Admur 447:60; M”A 447:38; Kneses Hagedola 96:2; Peri Chadash 94:21; Minchas Yaakov 61:6; Beis David Y.D. p. 16; Lechem Hapanim 96:7; Beis Lechem Yehuda 96:5; Chavas Daas 96:5 Biurim 1; Erech Hashulchan 96:5; Kaf Hachaim 94:60; 96:19
 See sources in previous footnote!
 See Rama 95:2; Taz 103:9 that if the Charif is a minority ingredient, then the mixture is not considered Charif. See next footnote
 As we consider it that the pot has absorbed the dairy taste carried in the onion, and it is hence similar to one who cooked dairy in a Non-Ben Yomo meat pot in which case we rule that the pot is nevertheless forbidden. [See Michaber 93:1; Shach 93:3 based on Rama in 94:5; Beis Lechem Yehuda 93:4; Chavas Daas 93:3; Kaf Hachaim 93:16; 94:54] Now, although the onion here is in minority, it is only its Charifus, and ability to extract non-Ben Yomo meat taste from the pot, which is negated, and not its ability to transfer taste into the pot. It is also similar to the case that a potato from a meat cholent was cooked in a dairy pot with other foods, in which case we rule that if there isn’t 60x versus the potato, the pot is forbidden even if it is not Ben Yomo. [See Rama 94:5 as explained in Shach 94:18; Taz 94:8; Toras Chatas 57:14; Chavas Daas 94:16; P”M 94 S.D. 18; M.Z. 7; Biur Hagr”a 94:18; Kaf Hachaim 94:52; See the following Poskim that by food we do not say Nat Bar Nat: Shaareiy Dura 60:3; Kneses Hagedola 95:26; P”M 93 S.D. 4; 94 M.Z. 1; 95 M.Z. 1; Chavas Daas 95:2; Kehilas Yehuda 95:1; Zivcheiy Tzedek 95:8; Kaf Hachaim 95:10; All the more so does this apply in this case, where we view the Charif as Beiyn of dairy.]
 See Rama 95:2; Taz 103:9 that if the Charif is a majority ingredient, then the mixture is considered Charif and hence extracts the meat taste from the pot, thus making everything forbidden.
 In such a case the onions become Chanan and it does not suffice to measure 60x versus the blade of the knife, or versus a Netila’s worth of the onion.