Preheat oven to 400 degrees. Brush two rimmed baking sheets with 1 tablespoon extra-virgin olive oil each. Arrange eggplant slices on sheets. Brush tops with 2 tablespoons oil and season with salt and pepper. Roast until eggplant is golden and tender, about 20 minutes. Let cool to room temperature.
On a serving platter, layer eggplant with sliced mozzarella and tomatoes. Top with basil leaves and drizzle with remaining 2 tablespoons oil and balsamic vinegar.