Cook the pasta according to the package directions until al dente. Before draining, reserve 1 to 2 cups of the pasta cooking water.
Melt 2 tablespoons of butter in a large skillet over medium heat.
Add the black pepper and cook for about 1 minute, stirring frequently, until fragrant.
Pour ½ cup of the reserved pasta water into the skillet. Add the drained pasta and the remaining tablespoon of butter. Toss to coat.
Reduce the heat to its lowest setting or remove the skillet from the heat. Add the Parmesan gradually, tossing continuously until it melts into the sauce.
Add more reserved pasta water, 1 or 2 tablespoons at a time, until the sauce is smooth, glossy, and creamy.
Serve immediately with additional Parmesan and black pepper, if desired.
