In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes, or until it becomes translucent.
Add the minced garlic to the pot and cook for an additional minute, stirring frequently to avoid burning.
Add the ground beef (or Italian sausage) to the pot. Break it apart with a spoon and cook until browned, about 5-7 minutes. Drain any excess fat.
Stir in the crushed tomatoes, broth, dried basil, dried oregano, red pepper flakes (if using), and season with salt and pepper. Bring the mixture to a gentle boil.
Once boiling, reduce the heat to a simmer and add the broken gluten-free lasagna noodles. Cook for about 10-12 minutes, stirring occasionally until the noodles are tender.
In a small bowl, combine the ricotta cheese, half of the mozzarella cheese, and half of the Parmesan cheese. Set aside.
Before serving, check the seasoning and adjust if necessary. Ladle the soup into bowls, adding a dollop of the cheese mixture on top.
Sprinkle with the remaining mozzarella and Parmesan cheese.
Optionally, garnish with fresh basil leaves before serving.