Pulse onions in a food processor until finely chopped. Remove. Pulse carrots, celery, and garlic until finely chopped.
Heat oil in a Dutch oven. Cook all chopped vegetables for 8-10 mins until soft.
Add ground beef, pancetta, salt, and pepper. Cook 5-10 mins, breaking up meat, until no longer pink.
Add wine; cook 1-2 mins until nearly evaporated.
Add broth, crushed tomatoes, and oregano. Bring to a boil, then reduce to a simmer. Cover partially and simmer for 1 hour 30 mins.
Stir in milk. Simmer partially covered for 35 mins more. Skim fat if desired.
Cook pasta in salted water. Reserve 1 cup pasta water before draining.
Toss drained pasta with the sauce, adding pasta water as needed. Garnish and serve with cheese.