Adjust oven rack to upper-middle position and heat oven to 500°F
Heat oil, garlic, and red pepper flakes in a large skillet over medium-high heat until fragrant, about 1 minute. Add tomatoes and cook until mixture is dry, about 10 minutes. Turn heat off. Stir in 2 tablespoons pesto and salt and pepper to taste.
Spread remaining pesto on insides of each roll and layer each roll with turkey, tomato mixture, and sliced cheese. Place sandwiches on baking sheet, with open sides facing up. Bake until edges of bread are golden and cheese begins to melt, about 5 minutes. Serve.