Heat the oil over medium-high heat in a large nonstick saucepot or Dutch oven. Add the sausage, onion, bell pepper, and garlic. Cook, stirring occasionally, until the sausage is crumbled and browned, 8 - 10 minutes.

Add the broth, tomato sauce, diced tomatoes, salt and crushed red pepper. Bring to a boil. Reduce the heat and simmer, stirring occasionally, until the flavors are blended, about 20 minutes. Add the noodles; bring to a boil. Reduce the heat and simmer, uncovered, stirring occasionally, until the soup thickens slightly and the noodles are tender, 10-12 minutes. Rove from the heat; stir in mozzarella, basil, and the Parmesan. Serve with the breadsticks, if using.