Bifteki me Tyri (με Τυρί) is the cheese-topped Greek patty: me tyri means "with cheese," and the distinction from the stuffed version is precise and physical. Here the cheese is not sealed inside the meat but melted over the top of an already-grilled bifteki, so it forms a browned, blistered cap rather than a hidden molten core. That single placement decision shapes everything about how the patty should be cooked and finished.
The build is the standard bifteki with a finishing step. The seasoned ground-meat patty, mixed with grated onion, bread binder, and oregano, is shaped flat and oval and grilled until it has a real crust and is most of the way cooked. A slice or scattering of cheese, often kasseri, graviera, or yellow tyri that browns well, is laid across the top in the last stretch of cooking, then the patty is covered or slid under heat so the cheese melts, slumps over the edges, and ideally catches a little color. Good execution adds the cheese late enough that it melts and tints without the meat overcooking underneath, leaving a juicy patty under a stretchy, lightly browned blanket that bonds to the surface. Sloppy execution drops cold cheese onto a patty that then sits too long waiting for it, drying the meat out, or uses a cheese that just goes greasy and slides off in a slick rather than melting into a cap.
Variations are mostly a question of which cheese and how it is finished. Kasseri and graviera pull into strings and brown at the edges; a softer cheese melts flatter and milder; some counters torch or grill-mark the top so the cap blisters, others keep it pale and just-melted. The patty then carries into a pita wrap or onto a plate, and the cheese-stuffed gemisto version, where the cheese is sealed inside instead, is a genuinely different build that deserves its own article rather than being crowded in here. What me tyri reliably promises is cheese as a visible, browned topping fused to the surface of the meat, not a surprise buried within it.