Heat a large nonstick skillet over medium-high heat, cook ground beef until browned, breaking it up as it cooks with a wooden spoon. Add the onion, green bell peppers and garlic and cook until soft, about 3 to 4 minutes.
Transfer to the slow cooker and stir in thyme, brown sugar, broth, diced tomatoes,stewed tomatoes, tomato sauce, Italian seasoning and salt. Cover and set the slow cooker to low 8 hours or high 4 hours.
About 30 minutes before the soup is ready, add the pasta, cover and cook until the pasta is cooked, about 30 minutes.
Serve in individual bowls with mozzarella cheese as a topping.