Preheat oven to 350°F.
Heat 2 tablespoons oil in a large skillet over medium heat until it shimmers, then cook shallot and garlic with ¼ teaspoon each of salt and pepper, stirring, until softened, about 5 minutes.
Increase heat to medium-high and add tomatoes, then cook, stirring occasionally, until softened, 4 to 5 minutes.
Transfer mixture to an 8-inch shallow baking dish.
Arrange cheese rounds on top, then sprinkle with piquillo peppers and salt and pepper to taste.
Drizzle with remaining 2 tablespoons oil.
Bake until cheese is just softened, 15 to 25 minutes.
