While the pasta cooks, grate the cheese either with a micro plane or a the fine side of a box grater. Reserve 2 cups pasta water and then drain the pasta.
In a large skillet, melt the butter over medium heat and add the pepper. Add half of the grated cheese while stirring and then add 2/3 cup reserved pasta water while consistently stirring.
Add the cooked pasta to the pan, using tongs to toss and mix in. Sprinkle in the remaining cheese with a tablespoon of the pasta water at a time until the sauce is creamy and the pasta is well coated.