Remove the stems of the mushrooms and pulse them in batches in a food processor. Mushrooms should be the size of large breadcrumbs, also resembling ground beef.
Chop the carrot, celery and onion into small ¼” dice. Mince the garlic finely.
Heat the oil in a large sauté pan over medium heat until it is starting to shimmer.
Add the diced carrot, celery and onion. Regulate the heat so that the vegetables soften slowly without browning. This will take 4 to 5 minutes.
Add the mushrooms and a large handful of fresh thyme or oregano leaves. Let this cook for a further 5-6 minutes. Stir it occasionally but not too often. The mushrooms will start by offering up their liquid and then dry and start to brown.
When the mushrooms have started to brown stir in the tomato paste followed by the milk.
Heat it to a simmer and taste. Add salt and pepper as needed.
Finish with ½ cup of hearty red wine.
Serve over fresh pasta. If you like you can stir in the fresh Parmesan and Basil or serve them on the side.