Heat the olive oil in a large pot or Dutch oven over medium heat.
Add the chopped onion and sauté for about 3-5 minutes until softened.
Stir in the minced garlic and cook for an additional minute.
Add the ground beef or turkey to the pot, breaking it apart with a wooden spoon, and cook until browned (about 5-7 minutes). Drain excess fat if necessary.
Pour in the crushed tomatoes, chicken or vegetable broth, Italian seasoning, salt, and black pepper. Stir to combine.
Bring the soup to a boil, then reduce heat and simmer for 10 minutes.
Add the broken gluten-free lasagna noodles and simmer for an additional 10-12 minutes, or until noodles are cooked al dente.
In a separate bowl, combine the ricotta cheese, half of the mozzarella cheese, and half of the Parmesan cheese.
To serve, ladle the soup into bowls and top each serving with a dollop of the ricotta mixture and a sprinkle of the remaining mozzarella and Parmesan cheese.
Garnish with fresh basil or parsley if desired.