Bring the 6 cups of water to a boil over high heat. Generously salt the water and once it comes to a boil, add the pasta and cook for 8 minutes.
About two minutes before the pasta is done cooking, heat a large skillet over medium heat. Add the butter and ground pepper and cook for 2 minutes.
Transfer the pasta to the pan with the butter and pepper. Toss to coat and gradually add the pasta water to the pan as it continues to absorb it. Remove the pan from the heat and add one cup of the grated cheese and immediately stir to create a creamy consistency.
Add a bit more pasta water if it starts to clump or dry. Serve immediately with more cheese and freshly ground pepper on top.