Sauté the aromatics: Heat olive oil in a large Dutch oven over medium heat. Add onion and cook until softened, about 5 minutes. Stir in garlic and cook for another 30 seconds until fragrant.
Brown the beef: Add the lean ground beef and cook until browned, breaking it apart as it cooks. Drain any excess grease.
Build the soup base: Stir in tomato paste and cook for 1–2 minutes. Add crushed tomatoes, diced tomatoes, and chicken broth. Season with Italian seasoning, basil, oregano, salt, and pepper. Stir well and bring to a gentle boil.
Simmer: Reduce heat and let the soup simmer for 15–20 minutes so the flavors can develop.
Add the noodles: Break lasagna noodles into small pieces and stir them into the soup. Simmer uncovered for about 10 minutes, stirring occasionally, until the noodles are tender.
Add the cream: Stir in heavy cream (optional) for a creamy texture.
Serve: In a small bowl, mix ricotta, mozzarella, and parmesan. Ladle soup into bowls, top each with a spoonful of the cheese mixture, and sprinkle with parsley.