Cook pasta until tender, 8-10 minutes. Drain & return to pot.
Meanwhile, heat oil in a large skillet over medium heat. Add veggies, and cook, stirring often, until mushrooms have released their liquid, 8-10 minutes. Add garlic and cook, stirring until fragrant, about 1 minute. Add sherry, scraping up any brown bits; bring to a boil and cook, stirring, until almost evaporated.
Whisk milk and flour in a bowl; add to the skillet with salt and pepper. Cook, stirring, until the sauce bubbles and thickens, about 2 minutes.
Stir in Asiago until melted. Toss the pasta and the sauce. Serve with more cheese, if desired.