Place the peppercorns in a mortar and pestle and crush them until you have a mixture of coarse and fine bits. (You can also grind them in a small food mill or coffee grinder.) Set aside.
Fill a large, heavy-bottomed pot with water and bring to a boil over high heat. Add 1 tablespoon salt and the pasta and cook according to the directions on the package until al dente. Ladle 1 cup of the pasta cooking water into a glass measuring cup and reserve it. Drain the pasta quickly in a colander and return the pasta to the pot with a lot of the pasta water still dripping.
Working quickly, with the heat on very low, toss the pasta with 1/2 cup of the grated Pecorino, the crushed peppercorns, cream, butter, parsley, and 1 teaspoon salt, tossing constantly. If the pasta seems dry, add some of the reserved cooking water. Off the heat, toss in the remaining 1/2 cup Pecorino. Serve immediately with a big bowl of extra grated Pecorino for sprinkling.