1. Heat 2 teaspoons olive oil in a small skillet, add the onion and 1 clove minced garlic. Saute until softened, about 5 minutes. Cool.
2. Combine the onion mixture with the ground turkey, lemon peel, parsley, sage, thyme, salt and pepper. Divide into quarters. Break the cheese slices in half and force 2 into the center of each section of turkey. Flatten and refrigerate until ready to use. (The cheese can also be put on top of the burgers when cooked.)
3. Stir together the remaining tablespoon olive oil and minced clove of garlic. Brush on one side of each bun.
4. Broil or grill the burgers on a lightly oiled rack until no longer pink in the center and the juices run clear. Place the buns cut side down around the edge of the grill to toast lightly, or toast under a hot broiler. Place each burger on a bun and serve with condiments.