Make sauce: In a dutch oven (or a 5-quart saucepan), heat oil over high heat. Add onions, carrots, and garlic; cook, stirring, until slightly softened, about 2 minutes. Add beef and pork; cook, breaking up meat with a spoon, until no longer pink, about 5 minutes. Stir in tomato paste; cook 1 minute. Season generously with salt and pepper.
Add wine and tomatoes. Bring sauce to a simmer; cook, partially covered, stirring occasionally, until thickened, about 1 hour. Add milk; simmer until completely absorbed, about 15 minutes more. Season again with salt and pepper.
When sauce is almost done, cook pasta in a pot of boiling salted water until al dente, according to package instructions; drain. Toss pasta with half the meat sauce; save remaining sauce for next day. Serve sprinkled with cheese.