It’s cheese from Cyprus that fries without melting and has a neat squeaky feeling when you chew it. It’s perfect sliced and sauteed in a skillet with some butter. Finish it with some lemon juice for the traditional Cypriot style. The dense texture makes it ideal for tossing into salads. Fucking love halloumi.
I had a cheese once at a greek/breakfast place in my hometown that they brought out on a sizzling skillet, poured liquor on, lit on fire, then doused with lemon juice. Was that perhaps the same? I think they called it "saganaki" or something similar though (no idea about correct spelling)
Saganaki is just a Greek appetizer made of frying cheeses, sometimes including halloumi, but not necessarily. The way you describe it is one typical way it’s prepared.