May one melt cheese on Shabbat (such as for making a grilled cheese sandwich?)
I don’t see that there may be a problem of cooking the bread. Is there a problem with melting the cheese or any other Shabbat violation that I may have overlooked?
There are a number of potential problems:
Cooking: it must be verified if the cheese was actually fully cooked in the production process. If not, bringing it to a temperature of Yad Soledes [about 110F] will violate the melacha of cooking.
Chazara: Even if there is no cooking involved, one may not put even cooked food directly on the fire or “blech” on Shabbos, because of the Rabbinic prohibition of Chazara. This could be circumvented by putting it on top of a pot or pan which is on the blech.
Melting: There is a Rabbinic prohibition of Molid, turning a solid substance into a liquid. Melting solid cheese may involve this prohibition, depending on how melted it will get.