Reusing a ladle to pour soup on Shabbos

Cooking after cooking by liquids-Taking a second portion of soup
 
It commonly occurs that after one uses a serving spoon or ladle to remove soup or another food from the Keli Rishon pot that was on fire the spoon or ladle is placed down on the counter. The question arises as to whether this spoon may be reused to take a second portion from that pot. The question at hand is regarding whether the liquid that remains on the spoon contains a cooking prohibition and thus may not be reinserted into the Keli Rishon pot which will heat it up.
 
 
On Shabbos, may one reuse a spoon or ladle to take a second portion from a pot of hot food?[1]
If the liquid on the spoon or ladle is still warm then it may be reused. If it has cooled down, then it must be dried prior to entering it into the pot, if the food in the pot is still Yad Soledes [110 degrees]. A piece of good advice to avoid this issue is to simply leave the spoon inside the Keli Rishon until everyone is done taking portions.
 
Background of reheating a precooked liquid that cooled off
 
Heating liquid that was previously cooked to the point of Yad Soledes:[2]
Important note: Wherever it is explained here that it is permitted to heat a food, it may only be heated through being on or very near a fire if the conditions that are explained in “The laws of Chazara” are fulfilled. See there! 
A precooked liquid that cooled below 110 Fahrenheit: All liquid substances are [forbidden to be] cooked [even] after having been previously cooked. Thus a liquid dish which was already fully cooked and cooled off, even if it did not cool off completely but is no longer [hot to the point of] Yad Soledes[3], if one heats it on Shabbos until it reaches [the heat of] Yad Soledes, he is liable for cooking.[4]
A liquid which is still 110 Fahrenheit or above: However if it [the precooked liquid dish] was [still] hot to the point of Yad Soledes and one then further heated it, there is no cooking [prohibition involved]. [Furthermore it] is allowed even initially to be [further] heated near a bonfire, although not very close to the fire, as will be explained. (Whether it is [also] allowed to be placed on a stove top was explained in the laws of Chazara).  
Other Opinions: [However] there are opinions[5] which say that even if [the precooked liquid] has [already] completely cooled down there is no [prohibition in] cooking it after [it having been previously] cooked, and it is thus allowed to be heated on Shabbos near a fire in a situation that no suspicion exists that one may come to stoke [the coals].
The Final Ruling:[6] The custom is to be lenient if [the liquid food] has not yet completely cooled down and is rather still fit to be eaten due to its heat[7]. However if it completely cooled down then we are accustomed like the first opinion….. regarding doing anything [to this liquid] which involves a cooking prohibition.
The law if one transgressed and re-heated cold liquid: If the liquid completely cooled down we are accustomed like the first opinion even regarding a case that one already heated it [and thus the food would be forbidden to be eaten] as was explained in chapter 253 [Halacha 25][8].
The law if one transgressed and asked a gentile to heat it near the fire[9]: (even if the Jew commanded the gentile to return it) if he returned it (even the Jew himself[10]) to an area where there are opinions which permit this to be done even initially, such as to place it near an oven[11] that is not swept or covered, or next to a bonfire, food that was completely cooked but has liquid which has completely cooled down, and [by placing it near the fire] it heated up there until it became Yad Soledes, then even though [transgressing such a prohibition according to some opinions] makes one liable to bring a Chatas offering (for the Jew) [if the Jew placed the food there], nevertheless, since there are opinions which allow this to be done even initially as will be explained in 318, [therefore] one may rely on their words after the fact (to not forbid the food placed on by the gentile, even if the Jew commanded him to do so).
Warming it up on a heater which will eventually turn on:  Even to place it on top of a heater prior to it being lit by a gentile in order for it to heat up when it gets lit is forbidden as explained there [in chapter 253 Halacha 27].
Practically[12]: Any food that was already fully cooked but cooled down a little, even though it is not hot to the point of Yad Soledes, [nevertheless] if it is [still] slightly hot to the point that it is edible due to its heat, the custom is to be lenient that [re-cooking] it does not involve the cooking prohibition and it is [thus] permitted to be placed on top of a hot pot or kettle [which is on a fire, even] in order to heat it a lot.
 
Summary of Re-cooking a precooked liquid:[13]
If is still Yad Soledes: Does not contain any cooking prohibition and thus is permitted according to all to cook by a fire [in ways explained in chapter 253] or to place in any pot of food that was heated on a fire and is now off the fire.
If is no longer Yad Soledes but is still hot enough to be eaten: The custom is to be lenient and allow it to be further warmed in the permissible ways explained in chapter 253.
If is cooled off to the point that it is no longer hot enough to eat: The custom is to be stringent that reheating contains a cooking prohibition [even after the fact and thus the food is forbidden to be eaten on Shabbos, Vetzaruch Iyun from 253]. If however a gentile heated it near a fire one may be lenient to eat it on Shabbos.