Bring 6 quarts of water to a boil in a large pot over high heat and add 4 tablespoons salt. Drop the pasta into the water. After 1 minute, when the pasta begins to soften, stir to prevent the pasta from sticking together and to submerge it completely in the water.
Cook according to the package directions for al dente, stirring occasionally. When the pasta is ready, remove 2 cups of pasta water and set aside. Drain the pasta through a colander.
Heat the oil in a large skillet over medium heat, then add 2 tablespoons black pepper and cook until the peppercorns begin to warm and become fragrant, about 30 seconds. Stir in 1/2 cup of the pasta water and then the pasta and stir. Pull the pot off the heat and add the Pecorino and Parmigiano, stirring and tossing vigorously until they melt and the sauce becomes creamy. If the mixture becomes dry, clumpy or stuck together, add more pasta water, 1/4-cup at a time, stirring and tossing until a creamy consistency is reached. (The pasta will thicken as it stands.) Add a little more pasta water at a time to loosen it back up again, if you like. (You might not use all of the pasta water.)
Serve immediately sprinkled with more Pecorino-Romano and black pepper.
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