Prepare the Bolognese Sauce. Heat olive oil in a large skillet or Dutch oven over medium heat. Add the onion, garlic, carrots, and celery and cook for 3-4 minutes until softened. Stir in the ground meat and cook until browned, breaking it up as it cooks. Add the tomato paste, stirring well to coat the meat and veggies. Pour in the crushed tomatoes, broth, and red wine (if using). Season with Italian seasoning, salt, and pepper. Let the sauce simmer on low heat for 30-40 minutes, stirring occasionally.
Cook the Gnocchi. Bring a large pot of salted water to a boil. Add the gnocchi and cook until they float to the surface (about 2-3 minutes). Drain the gnocchi and set aside.
Assemble the Dish. Stir the cooked gnocchi into the Bolognese sauce. Toss gently to coat the gnocchi in the sauce. Add a splash of heavy cream or milk (optional) for extra richness. Sprinkle with grated Parmesan and garnish with fresh basil or parsley.
Serve and Enjoy. Plate the gnocchi Bolognese and serve hot with extra Parmesan and fresh herbs.