I remember reading ‘Heidi’ when I was a kid, and drooling over the description of the Grandfather’s ‘grilled cheese’:
https://www.chowhound.com/post/cheese-detectives-cheese-featured-heidi-873259
We had Saanen dairy goats for over 25 years and I made hundreds and hundred of pounds of cheese, lots like what the Grandfather made. Other kinds too but that was my favorite and the easiest and the most versatile.
Looked at that post it’s too old to bother answering. It’s basically a fresh cheese, pressed not aged. Just think cultured curds pressed so it’s firm and dry enough. When heated it will melt or brown with no whey dripping out.