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Heat a large, heavy based saucepan over medium heat, add olive oil, onion, celery and carrot, sauté until tender. Add the garlic and sauté for a further 30 seconds.
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Add beef mince, breaking it up with a wooden spoon and cook until browned.
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Add eggplant and mushrooms and cook for 10 minutes.
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Add the tomato, milk, bay leaves, season well with salt and pepper and bring to the boil.
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Simmer the sauce for 1 hour, stirring occasionally.
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1o minutes before the sauce is due to finish, in a pot of boiling salted water, cook pasta as per packet directions.
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Return the cooked pasta to the pasta pot and pour over the bolognese sauce and add the
chopped parsley, stirring to coat the pasta.
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Serve pasta with grated parmesan.