Preheat oven to 400 degrees F (200 degrees C). Prepare a baking dish with non-stick play.
Arrange eggplant and tomato slices into the bottom of the prepared baking dish. Drizzle olive oil over the vegetables; season with oregano, salt, and pepper. Sprinkle Parmesan cheese over the entire mixture.
Bake in preheated oven until the cheese is beginning to brown, about 30 minutes. Switch oven broiler to high; continue baking until completely browned, about 5 minutes.
