Bring a large pot of salted water to boil over high heat. Add pasta and cook until al dente.
Meanwhile, in a large bowl, combine 1 1/2 cups of the Pecorino Romano, the pepper, and a small ladle of pasta cooking water. Using the back of a large wooden spoon, mix vigorously and quickly to form a paste.
When the pasta is cooked, use a large strainer to remove it from the cooking water and quickly add it to the sauce in the bowl, keeping the cooking water boiling on the stove. Toss vigorously, adjusting with additional hot water a tablespoon or two at a time as necessary to melt the cheese and to obtain a juicy sauce that completely coats the pasta.
Plate and sprinkle each portion with some of the remaining Pecorino Romano and pepper to taste. Serve immediately.