1. Bring 3 litres of water to a boil in a large pot. Season with salt; add pasta and cook, stirring occasionally, until about 2 minutes before tender. Drain, reserving 3/4 cup pasta cooking water.
2. Meanwhile, melt 2 tablespoons butter in a large heavy skillet over medium heat. Add pepper and cook, swirling pan, until toasted, about 1 minute.
3. Add 1/2 cup reserved pasta water to skillet and bring to a simmer. Add pasta and remaining butter. Reduce heat to low and add half the Parmesan, stirring and tossing with tongs until melted. Remove pan from heat; add the rest of the Parmesan, stirring and tossing until cheese melts, sauce coats the pasta, and pasta is al dente. (Add more pasta water if sauce seems dry.) Transfer pasta to warm bowls and serve.