Tanya Rudanovic, who is from Bosnia and waits tables at Stari Most in Astoria, said that the restaurant adds a little bit of fatty lamb  though she would not specify which part  to infuse the meat with flavor.

Elvis Kolenovic, an owner of Brothers Pizzeria in Long Island City who is originally from Montenegro, said that he grinds six different cuts together to arrive at the goal for both dishes: meat that is springy, savory and firmly gripped together.

Image SKINNY OFF THE GRILL The burger of the Balkans, pljsekavica, is served on a lepina, a pita-like bread, at Stari Most restaurant in Astoria, Queens. Credit... Evan Sung for The New York Times

Pljeskavica are formed from ground meat and minced onion, pounded thin, then grilled on both sides to a smoky brown. The word pljeskavica comes from pljesak, a regional word for clapping the hands, the motion used to press the burger into a thin round.

They were originally served flopped onto a plate, but as the American burger assumed global dominance, it became standard to sandwich pljeskavica between the two halves of a fluffy, spongy pita-style bread called lepinja.

These days, in Belgrade, the capital of the pljeskavica cult, the burger itself might be stuffed with mushrooms and mozzarella, or ham and cheese, as they do at Kafana.

Pljeskavica passion runs highest in Leskovac, the Serbian city considered the cradle of the dish. Each September, the town holds a weeklong rostiljijada, a grilling festival attended by hundreds of thousands of people. The festival’s high point is an annual attempt to set a world record for largest pljeskavica (last September’s record-breaker was more than four feet across, and weighed over 100 pounds).