Combine first 6 ingredients. Divide mixture into four portions. Indent center of each portion; place 1 1/2 tablespoons feta into each. Fold turkey mixture around cheese; shape each portion into a 1/2-inch thick patty.
Heat grill pan over medium-high heat. Coat pan with cooking spray. Add patties, cook 5 minutes on each side.
Combine cucumber, yogurt, and mint in a small bowl. Arrange 1 turkey patty, 1 tomato slice, 1 lettuce leaf, and 2 tablespoons yogurt mixture on bottom half of each roll. Top with top halves of rolls.