1. Bring a large pot of water to a boil. Cook noodles 5 minutes, gently stirring occasionally. Using a slotted spoon, transfer pasta to a bowl of ice water and let cool 20 seconds, then drain. Cut each noodle in half to make 12 squares.
2. Remove sausage from casings and mix it with half the garlic, 1 tablespoon Parmesan and parsley. With clean, damp hands, divide mixture into 4 meatballs; pat meatballs into 4-inch square patties, each about 1/2 inch thick.
3. Heat 1 1/2 teaspoons oil in a large nonstick skillet over medium-high heat. Add patties and cook until browned on both sides, about 5 minutes. Transfer to a plate using a slotted spoon and dispose of oil left in skillet.
4. Return skillet to stove; heat remaining oil over medium heat. Add onion, 1/4 teaspoon salt and 1/8 teaspoon pepper and cook until just golden brown, about 2 minutes.
5. Raise heat to high, add mushrooms and cook, stirring occasionally, until golden brown, about 5 minutes. Add remaining garlic; cook 1 minute more. Stir in wine, scraping the bottom of skillet. Add tomatoes and sugar; season with salt and pepper to taste. Add patties and simmer, stirring occasionally, until heated through, about 5 minutes.
6. Heat the broiler to medium high. Place 1 pasta square in the bottom of each of four shallow heat-proof bowls. Top with 3 heaping tablespoons sauce, 1 sausage patty, 1 slice mozzarella and 1 teaspoon Parmesan. Layer with a second pasta square, 3 heaping tablespoons sauce, 1 slice moz-zarella and 1 teaspoon Parmesan. Top with a third pasta square, 1 slice mozzarella and remaining Parmesan. Place bowls under broiler and cook until cheese is bubbly, about 1 minute.