Preheat the oven to 425 degrees F (220 degrees C).
Brush 2 tablespoons olive oil onto eggplant slices; arrange in a single layer in a shallow baking dish.
Bake in the preheated oven until eggplant is tender and browned, 20 to 25 minutes. Remove eggplant from the oven and reduce temperature to 350 degrees F (175 degrees C).
Heat 1 tablespoon olive oil in a large skillet or frying pan over medium heat; cook and stir onion, mushrooms, and garlic in hot oil until onion is softened, 5 to 10 minutes. Add tomato sauce, basil, and oregano; bring to a boil. Reduce heat and simmer until sauce is slightly reduced, about 10 minutes; season with salt and pepper.
Arrange about 1/2 of the eggplant slices in a 2-quart casserole dish; top with 1/2 of the sauce, 1 cup mozzarella cheese, and 1/4 cup Parmesan cheese. Repeat layering with remaining ingredients.
Bake in the preheated oven until hot and bubby, about 25 minutes. Cool for about 5 minutes before serving.
