In a large skillet, combine the onion, celery, carrot, and olive oil and cook over medium heat, stirring frequently, until tender, about 10 minutes. Add the meat and cook, stirring frequently, until it loses its pink color. Add the milk. Increase heat to high and cook until the milk has evaporated. Transfer the mixture to 4- to 6-quart heavy casserole. Return the skillet to the heat and add the tomato paste; cook over low heat to reduce its bitterness, about 5 minutes. Add the tomato paste to the casserole, along with the tomatoes, salt, and nutmeg. Cook the sauce over low heat, uncovered, for 2 to 3 hours. Stir frequently.