In a large pot or 6 quart Dutch oven, cook Italian sausage and onion in a couple of drizzles of olive oil. Cook over medium-high heat until no pink remains. Add garlic, cook for 1 minute longer. Drain any excess fat from the pot.
To the pot add beef broth, crushed tomatoes, diced tomatoes, tomato paste, Italian seasoning, salt, pepper and red pepper flakes. Bring to a boil, mix well. Cover and immediately lower heat to a simmer. Simmer covered for 15 minutes.
Uncover, add broken lasagna pieces and Parmesan cheese. Mix well. Simmer covered for another 15 minutes or just until the noodles are tender.
Uncover, check thickness. Add additional beef broth to thin or additional tomato paste to thicken to your taste.
Let stand uncovered for 5 minutes before serving. Serve topped with shredded mozzarella, a dollop of ricotta, grated Parmesan and parsley or basil.