In a large Dutch oven, combine ground chuck, onion, bell pepper and garlic. Cook over medium-high heat for 8 to 10 minutes, stirring occasionally until beef is browned and crumbles. Drain well.
Stir in thyme, brown sugar, broth, diced 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. Stir in Parmesan cheese.
Preheat broiler. Ladle soup into 8 to 10 ovenproof bowls. Evenly sprinkle with mozzarella cheese. Broil soups, 6-inches from heat, 3 to 4 minutes, until cheese is browned and bubbly. Add a garlic crostini slice on top. Serve immediately.
Preheat oven to 350 degrees F.
Cut bread into 1/4-inch round slices. Place on baking sheet and brush each slice with olive oil. Season with salt and pepper; place in oven and bake until golden and crisp, about 15 minutes. Remove from oven and let cool slightly. Rub each side with smashed garlic cloves.