Cook the pasta until al dente, according to the package directions. Drain and reserve ¾ cup of the cooking water.
Meanwhile, heat 2 tablespoons of the butter in a large skillet over medium-high heat. Sauté half of the mushrooms, stirring occasionally, for 7 minutes; transfer to a plate. Repeat with 2 tablespoons butter and the remaining mushrooms, transferring them to the plate with the rest of the mushrooms.
Add the shallots to skillet and cook until tender, about 5 minutes. Add the mushrooms back to the skillet, along with the wine; cook until the wine is reduced by half, about 3 minutes. Add the reserved cooking liquid and bring to a boil. Stir in the remaining 4 tablespoons butter and season with 1 teaspoon salt.
Reduce the heat to low and add the cooked pasta, cheese and parsley, tossing with the sauce until the pasta is coated and the cheese starts melting. Season with salt and pepper to taste. Serve immediately.