Bring a large pot of water to a boil and salt it. Cook the pasta until 2 minutes short of al dente. Reserve at least 1 1/2 cups pasta water before draining.
Toast the crushed pepper in a wide dry pan over medium heat for 60 seconds. Add 3/4 cup pasta water and simmer for 1 minute.
Make the Emulsion:
Place Pecorino in a bowl and stir in 1/2 cup warm, not boiling, pasta water a little at a time to form a smooth thick paste.
Transfer the pasta to the pepper pan and toss over low heat for 1 minute. Remove the pan from heat, wait 30 seconds, then add the cheese paste gradually while tossing vigorously.
Add small splashes of pasta water only until the sauce becomes glossy and clings to the noodles. Serve immediately with more pepper.
Notes
Add the cheese off direct heat; excessive heat makes Pecorino clump or turn stringy.
Cacio e pepe is best eaten immediately and does not reheat well.