Place feta cheese, 2 tablespoons olive oil, garlic, rosemary, and sea salt in a food processor and process until smooth. Transfer to a small bowl and drizzle with a small amount of olive oil (optional).
Heat a non-stick skillet or griddle to medium heat.
For each stack, spread a small amount of butter or olive oil on one side bread slices. For each stack, place one piee of bread buttered side down onto griddle or skillet. Top with mozzarella, turkey, and 2-3 tomato slices. Spread about two tablespoons of feta spread on the non-buttered side of another slice of bread and place feta side down onto the stack.
Grill until golden brown, then flip carefully and cook on other side. Remove to a plate and lift up one bread slice and add lettuce to grilled stack (if desired).