In a 12 inch skillet, brown hamburg, 1 onion, garlic, salt, and pepper. After mixture is browned, add tomato sauce, tomato paste, and 1/4 cup Parmesan cheese. Stir over medium heat until bubbly. Cover and set aside.
Fry 1 onion in 4 tablespoons butter until golden; set aside. In a 1 1/2 quart saucepan, blend milk, flour, and remaining Parmesan cheese. Stir constantly over high heat until thick and bubbly. Cover and set aside. Boil noodles 10 minutes; rinse. Lay out on a clean towel to drain. In a buttered 9x13" baking dish; layer 1/3 noodles, 1/3 meat sauce, 1/2 cheese sauce, 1/2 onions, and 1/3 Mozzarella. Repeat. End with noodles, meat sauce, and Mozzarella. Bake, covered, for 45 minutes at 350.