Heat olive oil in a large Dutch oven over medium heat. Add ground sausage and onion and cook until the onions have softened and the meat has browned. Break apart the sausage as it is cooking
Add the garlic and cook for an additional minute or until it is fragrant. Drain off any additional fat.
Add broth, tomato sauce, and diced tomatoes. Mix well and bring to a boil. Reduce heat and simmer about 15 to 20 minutes.
Meanwhile, break apart the noodles into 1 to 2-inch sized pieces. Add the noodles to the pot and simmer for an additional 10 minutes, stirring occasionally. Make sure the noodles stay covered in the liquid. Add more broth if needed.
Turn off the heat and stir in salt and pepper to taste. Add the shredded mozzarella cheese and stir until melted. Sprinkle basil on top before serving.