Place a large pot over the heat. Add the 1 pound ground beef, 1 small onion, diced, and 1 green bell pepper, diced. Cook while breaking the beef into crumbles until it is browned.
During the final couple of minutes of cooking, stir in the 3 cloves garlic, minced. Adding the garlic toward the end helps prevent it from burning.
Drain away the excess grease from the beef mixture, then return the ground beef mixture to the pot.
Add the 1 teaspoon ground thyme, 2 teaspoons Italian seasoning, ½ teaspoon salt, 1 Tablespoon brown sugar, 32 ounce carton chicken broth, 2 (14.5 ounce) cans petite diced tomatoes, and 15 ounce can tomato sauce. Stir everything together thoroughly and bring the mixture to a boil.
Lower the heat, cover the pot, and let the soup simmer gently for about 20 minutes.
After 20 minutes, stir in the 2 cups broken Mafalda pasta (or lasagna noodles). Continue simmering until the pasta is tender, about 10 or so minutes, stirring occasionally. The pasta can be broken into smaller or larger pieces according to preference.
Stir the ½ cup freshly grated Parmesan cheese into the finished soup.
Spoon the hot soup into individual bowls. If desired, finish each serving with shredded mozzarella cheese or a dollop of ricotta cheese.