Stirring Food On Shabbos

1. Stirring tends to accelerate the cooking process. Therefore, it is prohibited to stir a pot of partially cooked food or liquid. (S.A. 318:18)
2. Similarly, covering a pot hastens the cooking process. Thus, one may not cover a pot of partially cooked food. Therefore, if one uncovered a pot of food (such as cholent) and one realizes that the food is not fully cooked, one may not replace its cover (S.A. 254:4), unless the food is fully cooked. (See The Shabbos Kitchen page 9)
3. Stirring a partially cooked food is forbidden even if the food is off of the fire. (S.A. 252:1)
4. Interestingly enough, this prohibition extend to fully cooked food as well. Accordingly, one may not stir any food, cooked or uncooked, while over the flame, even if the flame is covered by a blech. (See Shar Hatzion 318:148 citing the view of the Kol Bo) When the food is off of the fire, cooked food may be stirred. (See Rama and M.B. 117 and Igros Moshe O.C. 4:74)
5. As cited above, one may not stir food that is on the fire, even if the food is fully cooked. The question is whether one may scoop food from the pot while still on the fire (dish out cholent) or is that considered stirring. The Mishnah Berurah writes that it is forbidden to do so. Therefore, one may not serve cholent directly from the pot if the pot is still on the fire. Rather, one must remove the pot from the fire and only then serve the food.
6. If the fire is not covered with a blech, since if he would remove the pot he would not be permitted to return it to the fire, (or if the pot is too heavy to lift or move), removing food with a spoon or fork from a pot of food which has been cooked completely may be permissible. (See Chazon Ish on M.B. and Halachos of Shabbos page 282. For a dissenting view see Igros Moshe O.C. 4:71) For normative halacha, a rabbi should be consulted.