Heat a dry saucepan and add the whole peppercorns. Shake the pan and toast until they are fragrant and almost translucent, about 2 minutes. Spread them out on a board to cool. Once they have cooled, roughly crush in a mortar with a pestle. Set aside.
Bring 5 cups of water to a boil. Add a large pinch of salt. (In this case, we are using less water than the amount recommended on the package. Why? Because as the pasta cooks, it releases starch into the cooking water. We want a higher than normal concentration of starch in the cooking water because we will use this to make our sauce. Don't worry, the pasta will cook just fine in this much water.)
Add the pasta noodles to the water and cook for 10 minutes.
As soon as the pasta is done cooking for 10 minutes, begin this step.In a medium saucepan, off the heat, add the grated Pecorino. Add a ladleful of pasta cooking water to the cheese, a little at a time, while stirring vigorously to melt the cheese. It's important to add the cooking water just a bit at a time while stirring constantly. The heat of the water will melt the cheese. Once the cheese is melted, stir in the crushed black pepper. Leaving a bit for the garnish at the end.
Using a large fork or slotted spoon, scoop out the pasta noodles and add them directly to the saucepan with cheese and pepper (so not drain). Stir to coat the pasta. (Note that we have not turned on the heat. The hot pasta water will heat the dish. When I have turned on the heat, it causes the cheese to stick to the pan.)
Serve immediately on a platter and top with more crushed black pepper and a healthy pinch of grated pecorino.