Preheat your oven to 375°F (190°C). In a large, sturdy pot or Dutch oven (that can go from stovetop to oven), heat the olive oil over medium-high heat. Add the onion, carrot, and celery (the mirepoix). Sauté until the vegetables soften, about 5 to 7 minutes.

Push the vegetables to the side, and add the ground beef. Break it up with a wooden spoon and brown it thoroughly. Once the meat is browned, drain any excess fat. Stir in the minced garlic and Italian seasoning, cooking for one minute until the garlic is fragrant.

Stir in the tomato paste, cooking it for a minute to deepen its color. Pour in the tomato sauce and the beef broth. Season with salt and pepper. Bring the sauce to a gentle simmer, then reduce the heat to low. Let the sauce bubble quietly for about 10 minutes to allow the flavors to marry.

Turn off the heat. Add the uncooked potato gnocchi directly into the sauce. Stir gently until every dumpling is evenly coated.

If you used an oven-safe pot, congratulations, you're halfway there! If you used a different pan, transfer the gnocchi and sauce mixture to a 9x13 inch casserole dish. Sprinkle the mixed mozzarella and parmesan evenly over the top.

Place the dish in the preheated oven. Bake for 20 to 25 minutes, or until the sauce is deeply bubbling around the edges and the cheese topping is melted, golden-brown, and crusty.

Let the cheesy gnocchi bolognese bake rest for 5 to 10 minutes after removing it from the oven. Garnish with fresh basil and a drizzle of olive oil. Serve hot.