In a large pot or Dutch oven, heat the olive oil over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon. If using sausage, cook until no longer pink. Add the chopped onion and garlic to the pot, cooking until softened, about 3-4 minutes.
Pour in the crushed tomatoes, beef or vegetable broth, tomato sauce, Italian seasoning, dried basil, salt, and pepper. Bring the mixture to a simmer. Break the lasagna noodles into smaller pieces and add them to the pot. Cook for about 10-12 minutes or until the noodles are tender, stirring occasionally.
Once the noodles are cooked, remove the pot from heat. Stir in the shredded mozzarella and grated Parmesan cheese until melted and well combined.
Ladle the soup into bowls and garnish with ricotta cheese, basil, or parsley if desired. Serve hot.