Step 1

In a 12-inch skillet over medium, toast the peppercorns, shaking the pan often, until fragrant, 2 to 3 minutes. Transfer to a spice grinder and let cool, then pulse until coarsely ground, 8 to 10 pulses. (Alternatively, transfer the peppercorns to a mortar, let cool and crush with a pestle until coarsely ground.) In a small bowl, toss together both cheeses.

Step 2

To the same skillet, add the spaghetti, placing the noodles parallel to each other in the center of the pan, then add 2 tablespoons of the cheese mixture and ½ teaspoon each salt and the pepper. Add 4½ cups water. Bring to a boil over medium-high and cook, uncovered and frequently moving the pasta about with tongs but keeping it submerged as much as possible, until just shy of al dente; when done, the pasta will no longer be fully submerged and there should be a fair amount of starchy liquid (at least 1 cup) in the pan. If the pasta is very underdone and the water is already quite reduced, add another ½ cup water and cook, stirring often, until just shy of al dente.

Step 3

With the pan still on medium-high, add about half of the remaining cheese mixture and toss until fully melted. Add the remaining cheese mixture in 2 more additions, tossing until melted after each. The liquid will have formed a thin sauce that pools in the pan. With the skillet still on medium-high, continue tossing the spaghetti until al dente and lightly sauced, with a small amount of creamy sauce (about ¼ cup) pooled in the skillet; the timing will vary based on how much liquid was in the pan before the first addition of cheese. But at this point, cooking should take a couple of minutes at the most.

Step 4

Off heat, toss in 1 teaspoon of the remaining pepper, then let stand for 1 to 2 minutes; during this time, the sauce will “tighten” a bit more. Toss again. Taste and season with additional salt, if needed. Offer the remaining pepper on the side.