Heat the oven to 425°F. Toss eggplant with oil and 1/2 teaspoon salt and roast on two sheet pans for 20 minutes. Reduce oven to 375°F and grease a 9-by-13-inch dish.
Cook rigatoni 2 minutes short of done and drain. Brown beef and onion, drain, add garlic for 30 seconds.
Stir in tomatoes, oregano, remaining salt and pepper and simmer 6 minutes, then fold in roasted eggplant and pasta.
Spread in the dish and top with mozzarella and Parmesan.
Bake for 30 to 35 minutes until bubbling and browned. Rest 10 minutes.