Question: Is it permitted to place a challah directly on the hotplate on Shabbos?
Answer:
Regarding placing food on the hotplate on Shabbos, there are two different aspects that need to be addressed: bishul and chazoro.
Regarding bishul, there is no prohibition on Shabbos to re-cook a solid food that has previously been cooked (Shulchan Aruch Siman 318 Se’if 4). It is also clear from the following Se’if (Se’if 5) that there is also no prohibition to roast/bake a solid food that has previously been roasted/baked, and the only prohibition is to re-cook a food with a different cooking process.
Returning to a challah, since it was originally baked, there is no further obligation of bishul/afiya to heat up the challah on a hotplate, because even if this reheating would be classified afiya, the rule is that ein afiya achar afiya.
Regarding chazoro, only a food item that was originally on the hotplate on Shabbos can be returned to a hotplate on Shabbos (provided that there are the necessary conditions of chazoro enumerated in Siman 253 Se’if 2).
Therefore, if the challah was not on the hotplate when Shabbos began, it cannot be placed directly on the hotplate on Shabbos (because of the Rabbinic prohibition of chazoro).
However, the challah can be placed on top of a pot of food that is already on the hotplate on Shabbos (c.f. Shulchan Aruch Siman 253 Se’if 5).