Preheat oven to 425F. Mix oil, vinegar, oregano, salt and pepper in a small bowl.
Spread eggplant and tomatoes in a single layer on a rimmed parchment-lined sheet. Brush with oil and vinegar mixture.
Bake until eggplant is tender, about 15 minutes.
Preheat broiler; arrange rack about 6 inches from top heat source. Stack tomato slice on top of eggplant slice, sprinkle with mozzarella. Broil until cheese melts, about 1 minute. Sprinkle with fresh basil leaves.