Preheat the oven to 350°F (175°C).
In a large skillet, heat the olive oil over medium heat. Add the diced onion and minced garlic, and sauté until softened, about 3-4 minutes.
Add the ground beef (or turkey) to the skillet. Cook until browned, breaking it apart with a wooden spoon, about 5-7 minutes. Drain excess fat if needed.
Stir in the gluten-free pasta, beef broth, diced tomatoes (with their juice), oregano, basil, salt, and pepper. Bring the mixture to a boil.
Reduce the heat and let it simmer uncovered for about 10 minutes, stirring occasionally, until the pasta is cooked and the liquid is mostly absorbed.
Transfer the mixture to a greased casserole dish. Sprinkle shredded cheese evenly on top.
Bake in the preheated oven for 15 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let it sit for 5 minutes before serving.