Bring a pot of salted water to a boil and cook pasta until al dente, about 7-8 minutes. Drain; reserve 3/4 cup cooking water.
Melt 2 tablespoons butter in a skillet over high heat. Sauté half the mushrooms until they brown, stir occasionally, about 7 minutes; transfer to a plate. Repeat with 2 tablespoons butter and remaining mushrooms, reserve with other mushrooms.
Add the shallots to the skillet and cook until tender, about 5 minutes. Add mushrooms and wine; cook until wine is reduced by half, about 3 minutes.
Add reserved cooking water; bring to a boil. Swirl in remaining 4 tablespoons butter. Season with 1 teaspoon salt.
Toss pasta with mushrooms, cheese, and parsley until pasta is coated and cheese starts melting. Season with salt and pepper.
