Heat the oil over medium heat in a 6 to 8 quart pot, until hot. Add the onion, celery, carrots, and 6 garlic cloves; cook for 5 to 10 minutes.
Add the pork, beef, and prosciutto. Increase to high heat, crumbling the meat into tiny pieces with the edge of a wooden spoon, until all the meat is browned. Stir in the tomato paste, tomatoes, milk, star anise, anchovies, thyme, and wine. Simmer for 90 minutes.
Check consistency of sauce. If it’s too thick, add ¼ cup water to thin it out.
Add 1 minced garlic clove to sauce and stir. Season with salt and pepper if needed.
Cook spaghetti for one minute less than the box directs. Drain in a colander and transfer back into pasta pan.
Add 3 cups of the meat sauce to the cooked pasta and toss to coat noodles. Serve with Parmigiano-Reggiano and garnish with chopped basil.