Step 1Heat the oven to 375 degrees. Grease a gratin dish or rimmed baking sheet with 1 teaspoon olive oil. Rub with garlic. Sprinkle with hot pepper. Set aside.
Step 2Lay 4 tomato slices down the center of the pan, leaving a couple of inches between them. Spoon one-fourth teaspoon olive oil on top of each tomato slice. Top with 4 slices mozzarella. Sprinkle with chopped basil. Season with salt and pepper to taste. Continue layering with the remaining tomatoes, olive oil, mozzarella, and basil making 4 tomato-cheese stacks.
Step 3Bake 10 minutes, until the cheese is starting to melt. Using a slotted spatula, carefully transfer each stack to a serving platter or plates. Drizzle each stack with one-half teaspoon balsamic vinegar and one-half teaspoon olive oil; top each with a basil sprig. Serve warm or at room temperature.