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Bring medium pot salted water to a boil.
Heat oil in large skillet over medium heat. Add mushrooms and Brussels sprouts and cook 8 to 10 minutes, stirring often, until mushrooms release their liquid. Add garlic and cook another minute, stirring, until fragrant; add vinegar, scraping up any brown bits; bring to boil and cook, stirring, until almost evaporated.
Once water is boiling, cook pasta, according to package directions.
Whisk milk and flour in a bowl; add to skillet with sea salt and pepper. Cook 2 minutes, stirring, until sauce bubbles and thickens. Stir in parmesan. Strain pasta and toss in sauce to coat. Serve with more grated cheese, if desired.