The test kitchen and Coastal Living staff agree that this is one of the best eggplant dishes we've eaten. The tomatoes can roast while you prepare the rest of this dish.
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.