Step 1

Bring 4 quarts of water and the salt to a boil in a large pot.

Step 2

Toast the black and Sichuan peppercorns, if using, in a large, high-sided skillet over medium-low heat, shaking the pan frequently, until fragrant, 1 to 2 minutes; transfer to a bowl, reserving the skillet.

Step 3

Melt the butter in the reserved skillet over medium-low heat. Add 2 teaspoons of the pepper mixture and cook, stirring, until the butter just begins to brown, 1 to 2 minutes. Add the chili crisp and cook, stirring occasionally, until the chili flakes become fragrant and sizzle, 2 to 3 minutes; remove the pan from the heat. (At this point the sauce can sit, covered, for up to 2 hours.)

Step 4

Add the pasta to the boiling water and cook for 1 minute less than the low end of the package instructions. Meanwhile, place the Pecorino in a large heatproof bowl and set aside. A few minutes before the pasta is done, transfer 1/2 cup of the pasta cooking water to the bowl with the Pecorino and whisk until no lumps remain.

Step 5

Use tongs to transfer the pasta directly to the skillet and place it over medium-high heat. Cook, stirring constantly, until any water has evaporated and the pasta is evenly coated with the chili mixture, 1 to 2 minutes.

Step 6

Immediately transfer the pasta to the bowl with the cheese mixture, scraping out the skillet. Add 1/4 cup of the pasta water and use the tongs to rapidly toss everything together until the pasta is well coated and the cheese is dissolved. (There should be extra sauce pooling in the bowl at first, but it should all cling to the pasta after 1 to 2 minutes of stirring. If the sauce looks too thick after 1 minute, add more pasta water 1 tablespoon at a time until smooth and creamy.)

Step 7

Transfer the pasta to a serving dish or individual bowls, sprinkle with more Pecorino and the remaining pepper mixture, and serve with more chili crisp, if desired.