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.
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.