In a food processor, combine the onion, carrot, and celery. Pulse until finely chopped.
In a deep, wide skillet over medium heat, melt the butter. Add the onions, carrots, and celery. Cook, stirring often, for 5 minutes, or until soft and translucent but not browned.
Add the ground beef to the skillet with the sautéed vegetables. Add the salt and pepper. Break the meat up with a fork or a potato masher and cook over medium heat for 3 to 4 minutes, mashing it until it is crumbly and no longer pink.
Add the milk to the skillet and simmer, stirring often, for about 4 minutes, or until the milk has almost completely evaporated. Stir in the nutmeg.
Add the wine to the skillet and continue to simmer for about 5 minutes, or until it has almost evaporated.
Pour the tomatoes into a bowl and squish them with your hands to break them up so there are no large pieces. Add them to the skillet and bring the sauce to a simmer. Turn the heat to low and simmer the sauce for 15 to 20 minutes, stirring occasionally, until the sauce is thick.
Serve the sauce over a bed of cooked pasta.
