Heat Dutch oven with olive oil over medium high heat. Add ground beef and prosciutto. Cook until brown, about 5 minutes.
While cooking, combine carrots, celery, and onion in food processor and pulse to chop finely.
Remove meat from pan and set aside. Add vegetables to dutch oven with a pinch of salt and sweat until aromatic, about 4 minutes.
Add meat back to pan. Add milk and simmer until almost fully reduced, about 10 min.
Then add tomatoes, wine, herbs & spices and let it simmer for about 30 minutes, until all flavors are well combined.
While sauce is simmering, bring pot of salted water to a boil.
Depending on if you are using fresh or dry pasta will determine when to drop it in the water. Generally fresh is 3-4 minutes and boxed pasta is about 8-10 minutes.
Drain pasta and reserve about 1/3 c. pasta water (possibly less if your sauce still contains a lot of liquid). Stir in pasta into sauce. Add pasta water and parmesan and continue to mix.
Remove from heat and serve.