Bishul 6

It is taught in a baraita: It is possible for several people to perform a single act of cooking on Shabbat, and all will be liable. How so? One brings the fire, and one brings the wood, and one places the pot on the stove, and one brings the water for the pot, and one puts spices into the food, and one stirs the pot; they are all liable for cooking. The Gemara wonders at this: But wasn’t it taught in a different baraita that the last one is liable and all the rest are exempt? The Gemara responds: This is not difficult. This case, where all are liable, is referring to a situation in which he brought fire at the outset, and therefore each of them performed part of the act of cooking; that case, where only the last one is liable, is referring to a situation in which he brought fire at the end. In that case, none of the earlier people performed any aspect of cooking at all, as the labor of cooking begins only from when fire is brought.

...stirring [is chayav] for cooking, for it is also an Av melacha.

(4) [In the case of] one who provided the fire, one who provided the wood, one who provided the stewpot, one who provided the water, one who provided the meat, one who provided the spices and one who stirred [in this sequence], they are all liable on account of cooking. As anyone who does one of the accessories of cooking is surely cooking. But if one first placed the stewpot on the stove, another one came and provided the water, another one came and provided the meat, another one came and provided the spices, another one came and provided the fire, another one came and provided the wood on the fire and another one came and stirred, only the last two are liable on account of cooking.

...the issur to stir, there are those who write that it is only forbidden [on the Torah level] the first time one stirs, because stirring it again doesn't cause it to cook quicker. Once it is stirred [the first time] it will cook either way, so you are exempt [on the Torah level] for what have you accomplished [by stirring it again]? The Ramban and Rashba were inclined to hold like this. Though certainly according to everyone, any situation which would not be a Torah prohibition to cook, you would also not be prohibited by the Torah to stir that food. Meaning, that if one was cooking a food that was fully cooked, it would not be a Torah level transgression to stir it according to the Rambam's opinion [about what level cooked is not cooking.] According to others, if the food was cooked to the level that it would be edible by Ben Drusai [under duress] stirring would also not be forbidden on the Torah level.

...and they need to be careful not to put the water into the pot while it is on the fire, since they mix and stir the contents of the pot in order that it be blended well, and we hold that one who stirs transgresses the Torah prohibition of cooking, even if the contents of the pot are cooked, the whole time it is on the fire. Though a pot which is off the fire, is not an issue to stir...

(11) It is forbidden to insert a ladle into a stewpot to remove [food] from it on Shabbat while it is on the fire, since he is [thereby] stirring it. And this is one of the auxiliaries of cooking, such that it is as if he is cooking on Shabbat. And it is permissible to return [food] from [one] stove to [another] stove – even from a stove the fumes of which are lesser to a stove the fumes of which are greater – but not from a stove to a covering nor from a covering to a stove.

The Ramach writes it is forbidden to put the ladle [into a pot] etc. - I would explain, this is talking about a food which was not fully cooked, though if it was fully cooked it is permitted, and that is the custom....

(18) 18. One may not spoon food from a cooking utensil or pot removed hot from the fire if the food is not fully cooked, because it is stirring. But if fully cooked it is permitted. However, wool in a dying tub (also hot), even if the wool is already dyed, is forbidden to stir (i.e. to stir with a spoon). RAMA: Initially one should be careful (not to spoon food) even from a pot of food in all circumstances. [Piskei Mahar”i Weil, known as the Mahariv]

even in a pot etc - rather you should empty the pot into a bowl and not remove the contents with a spoon/ladle. Analyze the Acharonim and see that the minhag is not to be machmir about this, for in truth the main halacha is like we wrote originally, that if the food is fully cooked even to stir it is permitted as is explained later on in Siman 121 at the end of seif 19. If one wants to be machmir, he should do so by actual stirring [not to stir] but to remove the food from the pit with a spoon/ladle he shouldn't be machmir at all if the food is fully cooked and off the fire.

(4) 4. Food fully cooked which has cooled down may not be reheated because of the Melacha of Bishul (cooking). RAMA some hold that this is only if the food is Mitztamek ve’yafe lo. [R' Yerucham] Food not fully cooked, even if cooked to the degree of Ma’achal ben Derusa’i and even if the food is hot, is nevertheless forbidden to cook any further. The reheating that is forbidden, only applies to food with liquid, but a cooked food item that is a solid (has no liquid), may be immersed in hot water on Shabbos. A solid food item that has not been cooked before Shabbos, may not be immersed into hot water on Shabbos, but one may pour hot water over it on Shabbos, with the exception of aged salted food and a fish called “Kulias ha’ispanin”, which do not require much cooking, and by pouring water over them one completes the Melacha. RAMA: This rule applies to all hard foods that cannot be eaten without first marinating them. Therefore one may not soak them (in hot water) on Shabbos, as it is a completion of a Melacha. [Ha'gahot Mordechai]

One may soak it - even in a kli rishon which is still boiling in order that the food will melt there and it will become a liquid for there is no [issur of] cooking an already cooked item. Though you shouldn't put it in a kli rishon that is on the fire.