We do something similar, but I’m super lazy. Basically, I do bread + mayo + shredded Mexican blend cheese, and microwave for 15 seconds or so until the cheese melts. If I’m not lazy, I’d butter the bottom of the broad and toast it on a pan w/ the lid on, so the bread gets a little toasty while the cheese melts.
We just call it “bread w/ cheese,” because every other combination has a different meaning (cheese bread has cheese in the dough, cheesy bread has crispy cheese on the outside, grilled cheese has slices of [usually] cheddar). It’s pretty good though, the cheese gets really melty, and it’s really fast since the cheese is shredded.
It sounds pretty similar to what you make, and I think it’s one of those “let’s whip something up” dishes that don’t get a proper name.
Ah yes, the daily ritual of trying not to starve.
Your laziness sounds delicious, though. If you had to give it a fun descriptive name for everyone to use, what would you call it?