Bring a large pot of salted water to a boil.
While the water comes to a boil, finely chop the onion, carrot, celery and mushrooms. (If you have a food processor, use it to chop each vegetable separately, and simply pulse to chop the mushrooms—you don’t want them to turn into a paste.)
When the water is boiling, cook the pasta according to package directions until just shy of al dente. Drain pasta.
While the pasta cooks, heat the oil in a large saucepan over medium-high. Add the onion, carrot, celery and a pinch of salt. Cook 5 minutes, or until tender, stirring occasionally. Stir in wine, scraping pan to loosen any browned bits. Cook 1-2 minutes, or until wine evaporates.
Stir in mushrooms. Stir in milk, and simmer 1-2 minutes until the milk has mostly evaporated. Stir in the tomatoes and Worcestershire. Bring to a simmer, and cook 5 minutes. Taste and adjust seasoning as needed. Add cooked pasta, tossing to coat. Let the pasta cook in the sauce 1-2 minutes, or until al dente. Serve garnished with cheese and, if desired, parsley.