Answer: The Shulchan Aruch (OC 318:4) writes that one may heat up a davar yavesh, dry cooked item of food on Shabbos, but not a davar lach, liquid food. There is a machlokes, however, as to how dry the food needs to be to allow it to be reheated.
The Pri Megadim (Mishbetzos Zahav OC 253:13) quotes some rishonim who define the issur of bishul as a food made up mainly of liquid which will improve through further cooking. Thus, he writes if the dish is mainly solid then it is considered to be a davar yavesh.
R’ Ovadia Yosef (Yabia Omer OC 7:42:6; OC 9:108:169; Yechave Daas 2:45) quotes other poskim who likewise maintain that if less than half of the dish is liquid, it is still considered to be dry and may be heated on Shabbos (See Kaf Hachaim OC 253:91; Har Tzvi OC 1 Mevashel:1)
The Shulchan Aruch Harav (OC 318:11), Mishna Berura (318:32) and R’ Benzion Abba Shaul (Ohr Letzion 2:30:13), however, define yavesh as having no liquid element to the dish. Thus, one wouldn’t be able to heat up any chicken or meat in a sauce, etc. R’ Moshe Feinstein (Igros Moshe 4:74:Bishul:7) writes that one should ideally follow this view.
Nonetheless, R’ Shlomo Zalman Auerbach (quoted in the Dirshu Mishna Berura 318:n37) maintains that the food doesn’t need to be totally dry, and even according to the Shulchan Aruch Harav, there would be no issue with heating up food with a little bit of thick sauce, such as ketchup.
In conclusion, one can heat up dry pieces of food, even if they have a little bit of thick sauce on them. One should avoid heating up food in gravy, however, unless absolutely necessary.