Toast the peppercorns in a hot, dry pan until fragrant, then roughly crush. Set aside.
Bring 6 quarts of salted water to a boil. Add some olive oil to the water, then add the pasta. Stir occasionally during cooking and cook until pasta is tender, 10 – 12 minutes, or to desired doneness. Drain pasta, reserving1½ cups water. Set aside to cool slightly.
Meanwhile, place the cheese and most of the pepper into a study bowl. Gradually beat in some of the pasta water to make a paste, adding more water to make a sauce the consistency of bechamel. Toss in half of the pasta coating the pasta. Keep adding pasta and water while tossing making a sauce that thickly coats each strand.
Transfer the pasta to a warm bowl, sprinkle with a little more pepper, and serve immediately.