1. Melt the butter in a 6 quart Dutch oven or stockpot set over medium heat.
2. Add the garlic, onion, carrot, and celery; cook until they begin to release their liquid – about 8 minutes.
3. Add the veal. Cook, stirring to help break the meat up, until it is no longer pink – about 5 minutes.
4. Add the broth; scrape up any browned bits from the bottom of the pot.
5. Add the lentils and tomatoes. Bring to a simmer, then reduce the heat to low. Cook for 2 hours, stirring occasionally. (If the sauce begins to thicken too much, loosely cover with a lid for the second hour.)Warm the milk, either in a second pot or by microwaving it for 45 seconds. Stir into the sauce; season with salt and pepper. Simmer an additional 30 minutes.To serve, gently ladle ¾ cup sauce over each serving of pasta.