Cut the eggplant in half and crosshatch each half (make diagonal lines in both directions to create diamonds). Drizzle olive oil and sprinkle salt and pepper on both sides of the eggplant, smearing it so it coats everything. Place the eggplants flesh side down on a parchment-lined baking sheet and place in the oven for 15 minutes. Turn over and bake for another 5 minutes, until the flesh is creamy.
Place the eggplant halves on a plate, flesh side up. Place the basil leaves around and place the cherry tomatoes and mozzarella balls over them. Drizzle everything with some more olive oil, salt, pepper, balsamic and oregano. Bon Appétit