Sauté onion, carrot, and celery in the oil over medium-high heat until they begin to soften—5 to 10 minutes.
Add garlic and sauté a few minutes more. Add beef and salt; sauté until beef is browned and broken into bits. Add wine and let evaporate. Add tomatoes; bring to a boil. Simmer for 45 minutes.
Break the tomatoes into small pieces as you stir the sauce occasionally. Add milk and continue cooking for 15 minutes.
Spoon generously over your favorite pasta. Add Parmigiano-Reggiano cheese to taste.