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Add oil to a large pot or Dutch oven along with the diced onion, carrot, and celery. Saute for 2-3 minutes, over medium heat. Add garlic cloves and mushrooms and continue sauteing for an additional minute.
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Push vegetables to the side of the pot and add ground beef. Cook for 6-7 minutes, or until almost cooked through. Crumble with a potato masher to break it apart into fine crumbles, if desired.
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Add ¾ cup of milk, white wine, tomato paste, salt, pepper, dried herbs, and nutmeg. Stir to combine, bring to a boil and then reduce heat to low.
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Simmer bolognese, uncovered, for a minimum of 1 hour or up to 2 hours for the best flavor. Make sure to stir the sauce every few minutes to prevent it from burning.
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Stir in the remaining ¼ cup of milk just before serving.
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Serve bolognese sauce over pappardelle, tagliatelle, spaghetti or zucchini noodles with a sprinkle of Parmesan cheese. Enjoy!