Preheat oven to 375°. Place eggplant slices on a jelly-roll pan. Top each with tomato half and 1 piece burrata or mozzarella. Bake at 375° for 7 minutes or until thoroughly heated and cheese starts to melt. Place on a platter, and drizzle oil over cheese. Top evenly with basil and Parmesan. Sprinkle with Pangrattato.