Combine pasta, water and salt in a 3-quart, high-sided saute pan. (Water should just barely cover pasta and measure 1 1/2 inches deep total.) Cover and set over medium-high heat.
When water reaches a boil, remove the lid and decrease heat to medium to maintain a simmer. Stir the pasta every minute or so, making sure the ends of the noodles stay submerged and that they aren't sticking together.
While the pasta cooks, begin the sauce. Combine 2 tablespoons of the black pepper, 100 grams of the Pecorino, all of the Parmesan and the olive oil in a large, deep mixing bowl. Work ingredients together with the back of a wooden spoon until a thick paste forms.
When the pasta has been simmering for 5 minutes, ladle 1 cup of the cooking water into a measuring cup then slowly drizzle 3/4 cup into cheese paste, mixing until smooth.
After the pasta has been cooking for 10 minutes start checking for doneness; you want it to be just barely al dente (see note) as there'll be some carryover cooking in the next step.
Use tongs to lift the pasta out of the cooking water and allow to briefly drain before adding to the cheese paste. Grasp the pasta with the tongs and stir vigorously for 2 minutes (really use a lot of elbow grease here -- this is not a light toss). The pasta will continue to release starch and the sauce will emulsify. Around a minute thirty you will see cheesy water magically transform into a proper sauce. If you find your sauce clumping, add a bit more of the pasta water and continue working the pasta.
Portion pasta into 4 bowls, top with reserved Pecorino and black pepper and serve immediately.
Few things in the culinary realm are worse than overcooked pasta, so if it's not ready the first time you taste it, keep checking every 30 seconds thereafter.