When the water is boiling, add 1 pound dried spaghetti and cook according to package directions until al dente. Drain the pasta, then transfer to the reserved skillet. Toss with tongs over medium-low heat until the noodles are coated with the browned butter. Add the cheese mixture, 1/2 teaspoon black pepper, and 2 tablespoons of the parsley, and toss to combine. Taste and season with more kosher salt as needed.