Is it permitted on Shabbos to put cholent (from the cholent pot, using a ladle) onto a plate that is slightly wet (from having eat a wet food such as pickles)?
It is permitted. Although there is controversy regarding pouring directly on to uncooked water, in this situation there are a number of lenient factors. The fact that it is not the normal way of cooking, it is a minute amount, the fact that you don’t care even if the water would get cooked, (psik reisha dlo nicha leh), the fact that a ladle is considered a kli rishon is controversial, and if it is only a kli sheini it can’t cook liquids. Additionally, the fact that the cholent might be considered a solid is not at all clear, since it has liquid in it, and even if it would be a solid, a solid in a kli sheini is controversial if it is considered to be like a kli rishon. Due to all of these factors there is no need to be concerned about it. Additionally, (depending on the circumstances), it is possible that the juice got cooked in the plant that produced it, during the pasteurizing process.
Mishna Berura 253-84,Shmiras Shabbos Khilchoso 1 ftnt. 201, Divrei Yatziv O:CH156, Tzitz Eliezer 13-40, Mishne Halachos 6-67. Shevet Halevi 7-42(2), Igros Moshe O:CH 4-74 Bishul 5, Poskim.