Fill a pasta pot or a large stockpot with 6 quarts of water, add 6 tablespoons of salt, and bring the water to a boil over high heat.
Drop the pasta into the boiling water, stir to prevent it from sticking together, partially cover the pot and cook the pasta until it’s al dente.
While the pasta is cooking, combine the olive oil, pepper, and ½ cup of the pasta cooking water in a large sauté pan.
About 1 minute before the pasta is done, place the sauce over high heat.
Lift the pasta out of the cooking water, or reserve 1 cup of the water and drain the pasta, and immediately add the pasta to the pan with the sauce.
Cook the pasta with the sauce for 2 minutes, stirring with a rubber spatula or tongs.
Turn off the heat and let the pasta rest in the pan for 1 minute.
Add the grated Parmigiano-Reggiano and pecorino romano, stirring vigorously until the oil and cheese form a homogenous sauce.
Drizzle the finishing-quality olive oil over the pasta and stir quickly to combine.
Use tongs to lift the pasta out of the pan and onto the center of each plate, twirling it to form a tight mound.
Spoon any sauce left in the pan over the pasta and coarsely grind black pepper over the pasta, if desired, and serve.
