Heat olive oil in a large pot over medium heat. Add ground beef (or sausage) and cook until browned, breaking it apart with a spoon. Drain excess fat if needed.
Add diced onion and cook until softened (~3 mins). Stir in garlic, oregano, basil, and red pepper flakes; cook for 1 minute until fragrant.
Mix in tomato paste, then add crushed tomatoes and broth. Bring to a boil, then reduce heat and simmer for 15 minutes.
Add broken lasagna noodles and simmer for 10–12 minutes until al dente. Season with salt and pepper.
In a small bowl, mix ricotta, mozzarella, and Parmesan.
Ladle soup into bowls. Top with a dollop of cheese mixture and fresh basil.