In a large skillet over medium-high heat, brown the ground beef and diced onion for 6–7 minutes. Drain excess fat, then stir in garlic, tomato paste, and Italian seasoning for 1 minute.
Transfer beef mixture to a 6-quart slow cooker. Stir in crushed tomatoes, diced tomatoes, and beef broth. Cover and cook on LOW for 6–7 hours or HIGH for 3–4 hours.
Turn slow cooker to HIGH, stir in the broken lasagna noodles, cover, and cook for 25–30 minutes until tender.
Mix ricotta, Parmesan, and half of the mozzarella in a bowl. Ladle soup into bowls, top with a scoop of ricotta mixture, remaining mozzarella, and fresh basil.