Heat oil in a dutch oven over medium heat. Add the onion, carrot, celery and cook, stirring with a wooden spoon, until the vegetables are soft, about 8 minutes. Add the beef and prosciutto and season with a bit of salt and pepper. Cook over high heat until meat is browned.
Add wine and scrape any browned bits from the bottom of the pan. Cook until wine is almost all evaporated. Add the tomatoes with their juices and the beef broth. As soon as the tomatoes start to bubble, reduce heat to a gentle simmer, partially cover the pan, and cook, stirring every 30 minutes or so, for 1 1/2 hours. At the end of cooking the sauce should be a rich reddish color and a medium thick consistency. Taste and adjust seasoning to taste and turn off heat.
Bring a large pot of water to a boil. Add the fettuccine and 1 tablespoon coarse salt. Cook until al dente. Drain and place pasta in a large bowl. Add half the sauce, 1 tablespoon butter, and a handful of parmesan. Toss until pasta and sauce are well combined. Stir in more sauce if needed. Serve immediately with remaining parmesan on the side.