I like a combo of black and pink pepper because they hit different notes on the tongue and the back of the palate.
In a small skillet, toast the peppercorns over medium heat until fragrant, about 3 minutes. Transfer to a mortar and pestle and crush until coarsely ground. (Or place the peppercorns on a cutting board and press with a heavy skillet until coarsely ground.)
Bring a large pot of water to a boil. Salt the boiling water and add the pasta. Cook until 1 to 2 minutes shy of al dente.
In a large skillet, bring about 1 1/2 cups water to a low boil.
Just before draining the pasta, scoop out about 1/2 cup of the starchy cooking water. Drain the pasta. Whisk the cornstarch into the reserved cooking water to make a slurry. Whisk the slurry into the skillet of boiling water. Whisk in the cheese. Cook, whisking often, until the sauce thickens, 3 to 4 minutes.
Off heat, add the pasta and three-quarters of the crushed peppercorns to the sauce; toss until the pasta is well coated, about 2 minutes. Twist the pasta into large swirls. Divide among bowls. Top with the remaining crushed peppercorns.
Mastering a cheese sauce can be challenging. Just add cornstarch to stabilize it. Foolproof!