In a medium-sized pot, bring the water and salt to a boil. Add the pasta, breaking it in half if necessary to get it to fit into the pot. Boil the pasta according to the time listed on the package directions for al dente pasta. Before you drain it, set aside 1 cup of the pasta cooking water. Editor's Tip: Don't over-salt the pasta water! Since you'll be saving your pasta water, adding too much salt can cause the final dish to be too salty.
While the pasta cooks, melt half of the butter in a large skillet. Choose a skillet large enough to hold the pasta later. Add the freshly ground black pepper and cook for a minute, swirling the pan as you go. Toasting the black pepper infuses the butter with flavor and removes the pepper's sharp, spicy edge.
Add ½ cup of the reserved pasta water to the skillet and bring the mixture to a simmer. Add the cooked pasta and toss to combine, cooking it for a minute to warm the noodles through.
Remove the skillet from the heat and add the remaining butter and Parmesan cheese, stirring constantly until the cheese is fully melted. Add additional pasta water if the sauce seems too dry. Season the pasta with salt and pepper and serve each portion with extra grated cheese, if you like. Editor's Tip: Use a Microplane to grate the cheese for this recipe. If you don't have one, use the smallest side of a box grater; do not use pre-grated cheese because it won't melt into the sauce quite right.
