In a large stock pot, combine ground beef (or turkey), onion, and garlic. Cook over medium-high heat for 8 to 10 minutes, stirring occasionally until beef is browned and crumbles. Drain well.
Stir in brown sugar, broth, crushed tomatoes, tomato sauce, Italian seasoning, and salt. Bring to a boil over medium-high heat; reduce heat and simmer 20 minutes.
Add noodles, and simmer until noodles are tender (about 15 minutes). Stir in Parmesan cheese.
Preheat broiler. Ladle soup into 6 to 8 ovenproof bowls.
Sprinkle each bowl with 1/4-1/3 cup mozzarella cheese. Broil soups, 6-inches from heat, 3 to 4 minutes, until cheese is browned and bubbly.