Preheat oven to 425˚F.
Add olive oil to a large skillet over medium heat. Once hot and the oil is shimmering, add onions and carrots. Season with salt and pepper, cooking until softened, about 5 minutes, stirring occasionally.
Stir in pork, beef and garlic, cooking until beef has browned all over, about 8 to 10 minutes. Stir in tomatoes, tomato paste, milk, wine, bay leaf, and oregano. Simmer the sauce for 15 minutes, until the mixture has slightly thickened.
Stir in gnocchi and 1/3 cup water. Bring sauce to a boil, cooking for another 5 to 10 minutes.
Remove from heat and remove bay leaf and oregano sprigs, discarding them. Top with cheese and place in the oven.
Bake for 15 minutes, until sauce is bubbly and cheese has melted.
Top with freshly chopped basil leaves and grated parmesan, if desired.