In a large pot or Dutch oven, heat the olive oil over medium heat. Add the ground beef or turkey and cook until browned, breaking it apart with a wooden spoon, about 5-7 minutes.
Add the diced onion and minced garlic to the pot. Sauté for an additional 3-4 minutes until the onion is translucent.
Stir in the crushed tomatoes, tomato sauce, chicken or vegetable broth, Italian seasoning, salt, and black pepper. Bring the mixture to a boil.
Once boiling, stir in the gluten-free pasta shells or broken lasagna noodles. Reduce the heat to a simmer and cook according to the pasta package instructions, usually about 10-12 minutes.
In a separate bowl, mix together the ricotta cheese, mozzarella cheese, and grated Parmesan cheese.
Once the pasta is cooked, remove the pot from heat and dollop the cheese mixture into the soup, stirring gently to combine.
Serve hot, topping each bowl with extra shredded mozzarella and a sprinkle of fresh basil or parsley if desired.