In a large bowl, combine ground lamb, minced garlic, chopped rosemary, salt, and black pepper. Mix gently until all ingredients are well incorporated, being careful not to overwork the meat.

Form the Patties

Divide the mixture into 4 equal portions and shape each portion into a patty about 1 inch thick.

Cook the Patties

Heat olive oil in a grill pan or skillet over medium-high heat. Cook the lamb patties for about 4-5 minutes on each side, or until they reach an internal temperature of 160°F (71°C).

Assemble the Burger

To assemble, place a lettuce leaf on the bottom half of each burger bun. Add the cooked lamb patty, a slice of tomato, crumbled feta cheese, and a generous dollop of tzatziki sauce. Top with the other half of the bun.

Serve

Serve immediately with your favorite side dishes.