In large dutch oven, bring 2 quarts salted water to a boil. (Note: Use as little boiling water as possible; it will become a thick, starchy liquid that enhances and binds the sauce.) Once water is boiling, drop in pasta and give on initial stir after pasta is completely submerged.
While pasta cooks, set a sauté pan over medium heat and add peppercorns. Toast until fragrant, then add butter. Let butter melt and bubble with pepper, adjusting flame so that butter is bubbling right when pasta hits al dente.
When pasta is al dente, remove from water with tongs and drop into sauté pan. Ladle another 2 ounces pasta water into sauté pan and stir. Add cheese, stirring vigorously until a silky sauce forms between butter, starch water, and cheese. Season to taste with salt, then serve immediately.
*Tellicherry peppercorns can be found in Whole Foods stores and ordered online. You can sub grocery-store black peppercorns, but the finished dish won't have quite the same punch.