Halacha forbids stirring food in a pot that is on the fire or a blech on Shabbat. T
The Shulchan Aruch does, however, permit serving on Shabbat from a pot that is over the fire or on a blech. Thus, for example, if one does not want to take the pot of soup off the fire because he needs to keep it there until Shabbat morning, he may serve from the pot even while it is sitting on the fire. Since serving involves merely taking some soup or food with the ladle, and not mixing, it is permissible. One must ensure, however, not to mix the contents of the pot as he serves, such as by taking specifically from the bottom of the pot or moving the ladle around in search of a particular item.
Shulchan Aruch, Siman 252:1
See Menuhat Ahava, Helek 2, Page 348