Heat the olive oil in a large Dutch oven or soup pot over medium-high heat. Add the ground beef and onion. Cook for 7 to 9 minutes, breaking the beef into small pieces, until the onion has softened and the beef is browned and cooked through. Drain excess fat if needed.
Reduce the heat to medium. Add the garlic, tomato paste, Italian seasoning, and red pepper flakes, if using. Stir for 1 to 2 minutes, until the tomato paste darkens slightly and the garlic smells fragrant.
Pour in the crushed tomatoes and beef broth. Stir well, scraping the bottom of the pot. Add the salt and black pepper. Bring to a gentle boil.
Stir in the broken lasagna noodles. Reduce the heat to maintain a steady simmer. Cook uncovered for 10 to 15 minutes, or until the noodles are tender, stirring often. Cooking time will vary by noodle brand and how large you break the pieces.
While the noodles cook, stir together the ricotta, Parmesan, and basil or parsley in a small bowl.
Taste the soup and add more salt or pepper if needed. If it has thickened more than you like, stir in additional warm broth a little at a time.
Ladle into six bowls. Top each serving with mozzarella and a spoonful of the ricotta mixture. Add more Parmesan and fresh basil, if you like. Serve hot.