Preheat oven to 400 degrees, with racks in upper and lower thirds. In a 9-by-13-inch baking dish, combine tomatoes, 3/4 cup feta, 2 tablespoons olive oil, garlic, and sugar. Season with pepper. On a rimmed baking sheet, arrange baguette slices in a single layer; brush with 2 tablespoons oil.
Place bread on top rack and tomato mixture on bottom rack. Cook until bread is toasted and tomatoes have softened, 10 to 12 minutes. Top bread with tomato mixture, 3/4 cup feta, and basil.
Drizzle with 1 tablespoon oil; season with salt and pepper.