Cook pasta in a pot of salted boiling water until al dente, about 7 minutes. Drain; reserve 3/4 cup cooking water.
Heat 2 tablespoons butter in a skillet over high heat. Brown half the mushrooms, stirring occasionally, about 7 minutes; transfer to a plate. Repeat with 2 tablespoons butter and remaining mushrooms; transfer to plate. Add shallots to skillet; 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.