Bifteki Gemisto se Pita takes the cheese-stuffed Greek patty and commits it to a wrap: a gemisto bifteki, filled with feta or kasseri, folded into a pita with the standard street-counter dressing. The phrase se pita means "in pita," and it changes the dish from a plate item into something held in one hand and eaten walking. The defining tension is that the patty already hides a molten core, and the bread now has to manage that release without going soggy or splitting open.
The build runs in the order the counter works it. The stuffed patty is grilled first, sealed around its cheese center so the inside stays liquid while the outside crusts, then the pita is warmed briefly on the same surface so it turns pliable and faintly toasted rather than dry and cracking. The hot patty is laid on the bread, often sliced once so the cheese can move, then dressed: sliced tomato, raw onion, a few fries pressed in for starch and crunch, and tzatziki or a yogurt smear. The wrap is rolled tight and the base twisted or papered so it holds. Good execution times the cut so the cheese is still flowing when the pita closes around it, and the yogurt and tomato sit against the meat rather than soaking the bread from the outside in. Sloppy execution wraps a patty that has gone cold and stiff, so the cheese is a dense plug instead of a release, or overloads the sauce so the bottom of the pita tears halfway through.
Variations sit in the dressing and the bread. Some counters keep the pita thick and griddled like a flatbread; others use a thinner, more flexible round. The fries can be inside or skipped, the sauce can run to spicy pepper rather than yogurt, and a second cheese can be melted over the patty before it goes in. The stuffed patty served on a plate, or the plain unstuffed bifteki in bread, are close relatives that each deserve their own article rather than being crowded in here. What this version reliably promises is a hidden core of hot cheese delivered inside a wrap built to keep it intact until you bite.