My mother-in-law used to make Chicken Paprikash, and she would usually burn the rice at on the bottom of the pot. Her three sons, my husband being the youngest would fight over it. There was a name for the burned rice at the bottom of the pot, but I can't remember what she called it and neither can anyone else. I don't know what to tell my grandchildren! What is it called?
Sorry, the best I could come up with is a partial answer.
Tah-dig is the Persian/Farsi/Iranian name for the equivalent of what you describe - the crispy rice crust left at the bottom of the pot. It isn't usually "burned", per se, not carbonized, but rather golden brown and crisp, is only called overcooked or burned compared to the rest of the rice. It is very highly prized. The same technique, or texture, can also be found in some potato dishes, or even spaghetti, where the bottom-most layer is allowed to adhere to the pot after draining the cooking water, and become crisp and brown with added oil - very similarly to a western dish having the top deliberately browned in an oven, even if it was cooked stove-top previously.
The Iraqi version is named hikakeh. This is served in pieces (unlike tah-dig, which is served as a single thick crust) and is a slightly looser layer. The wikipedia article on hikakeh cites an encyclopedia of Jewish food, so it might be a starting place for to look for a yiddish version of the dish or name.
Beyond those two, I looked up and found Nurungji, the Korean version, Guoba which comes from the chinese, and cơm cháy for the Vietnamese, Okoge in Japan, and Cucayo (or pegao, concolon and others) along the Caribbean coast. The translation of each dish tends to be something like scorched rice, or toasted rice, or bottom-of-the-pot rice, and refers to the the way the bottom-most layer of rice tends to overcook in traditional cooking (ie, over a fire), and which later becomes sought after in its own right - and can be extended to non-rice dishes with a bottom crust.
Unfortunately, I was unable to find a specific name for the Hungarian, Yiddish, or Ashkenazi versions of the dish. If none of the above names are familiar to you, or you don't want to just pick one and go with it, they still might serve as a starting point for a) how to make the dish, if you want to recreate it, or b) how to ask for the name among the people in those communities (it's a bit easier to "translate" a dish name than to start from raw description, I found the above names because I knew about tah-dig).