Mix together yogurt, feta cheese, mint and pepper; set aside.
Divide the ground meat into 12 equal portions. Shape each portion into a thin pattie, about 4-inch wide. Place one Tbsp. of the yogurt feta mixture onto 6 of the patties, then top with the remaining meat patties, being careful to seal the mixture in.
Grill or broil the stuffed burgers for about 5-8 minutes, turning once. Serve immediately on the split pitettes (or rolls) with a slice of tomato and remaining yogurt sauce.