To a food processor, add the mushrooms, and pulse until they are chopped and resemble ground beef. Add to a bowl.
To the same food processor, add the onion, celery and carrot. Pulse until finely chopped and add to the mushrooms.
To a large, wide pan or a large high-sided skillet. Add the oil over medium-high heat. When the oil is hot, add the mushrooms, carrot and celery. Cook while stirring. The mushrooms will produce liquid, cook until the liquid evaporates, about 10 minutes. You may need to lower the heat as the liquid evaporates so it doesn’t burn on the bottom and stir often.
Add the garlic, salt, pepper and tomato paste. Cook for a minute, stirring until any liquid has evaporated. Add the wine, stir and allow to cook and reduce slightly for about 3 minutes. Add the puréed tomatoes/passata, milk, stock and mix well. Simmer for 30 minutes, stirring often to prevent sticking to the pan.
10 minutes before the end of cooking, stir in the Parmesan cheese. Taste for seasoning adjust if needed.
Serve with your favorite pasta.