Preheat the oven to 400 degrees F.
Lay the tomato slices flat and season with salt and pepper. Drizzle with 1 1/2 tablespoons of the olive oil. Arrange the tomatoes in a 10-inch oval baking pan. Sprinkle the basil pieces on top.
Combine the cheese, breadcrumbs and thyme in a small bowl. Sprinkle the tomatoes with this mixture and drizzle the entire mixture with the remaining 1 1/2 tablespoons olive oil. Bake the gratin until the top is golden brown, about 15 minutes. Serve.