Step 1: Prepare the Bolognese Sauce

1. Heat Olive Oil: In a large skillet or saucepan, heat the olive oil over medium heat.
2. Sauté Onion, Garlic, Carrot, and Celery: Add the chopped onion, garlic, carrot, and celery. Sauté for 5-7 minutes, until the vegetables are soft and fragrant. This mixture, known as soffritto, is the aromatic base of the sauce and provides depth of flavor.
3. Cook the Ground Beef: Add the ground beef to the skillet, breaking it up with a spoon as it cooks. Cook until browned, about 5 minutes. Drain any excess fat if necessary.
4. Add Tomatoes, Tomato Paste, and Broth: Stir in the crushed tomatoes, tomato paste, and beef broth. Mix well to combine.
5. Season and Simmer: Add oregano, basil, red pepper flakes (if using), salt, and black pepper to taste. Let the sauce simmer for 20 minutes, stirring occasionally, until it has thickened.
6. Finish with Milk: Stir in the milk or heavy cream to add richness and balance to the sauce. Let it cook for another 5 minutes, then taste and adjust the seasoning as needed.

Step 2: Cook the Gnocchi

1. Boil the Gnocchi: Bring a large pot of salted water to a boil. Add the gnocchi and cook according to package instructions (typically 2-3 minutes, until they float to the surface).
2. Drain and Set Aside: Drain the gnocchi and set them aside while you finish the sauce.

Step 3: Assemble the Gnocchi Bake

1. Combine Gnocchi and Sauce: Add the drained gnocchi to the skillet with the Bolognese sauce, stirring to coat each piece of gnocchi in the sauce.
2. Transfer to Baking Dish: Pour the gnocchi and sauce mixture into a greased 9×13-inch baking dish, spreading it out evenly.
3. Add Cheese: Sprinkle the shredded mozzarella and grated Parmesan evenly over the top of the gnocchi mixture.
4. Add Optional Dollops of Ricotta: If using ricotta cheese, add small dollops across the top for a creamy finish.

Step 4: Bake the Gnocchi

1. Bake: Preheat your oven to 375°F (190°C). Place the baking dish in the oven and bake for 20-25 minutes, until the cheese is melted and bubbly.
2. Broil for Extra Browning: If desired, broil the dish for an additional 2-3 minutes at the end of baking for a golden-brown, bubbly cheese top. Keep an eye on it to avoid burning.

Step 5: Garnish and Serve

1. Garnish: Remove the gnocchi bake from the oven and garnish with fresh basil or parsley for added color and flavor.
2. Serve Hot: Scoop generous portions onto plates and enjoy with garlic bread or a side salad.