In a small skillet, cook the guanciale over moderately low heat, stirring occasionally, until the fat is rendered and the meat is tender, about 15 minutes. Let cool slightly.

Meanwhile, in a large pot of salted boiling water, cook the pasta until al dente. Drain, reserving 1 cup of the cooking water.

In a large bowl, whisk the egg yolks and egg with the guanciale and the rendered fat. Add the pasta, 1/4 cup of the reserved pasta water and 2/3 cup of the cheese to the egg mixture and toss until creamy, about 1 minute; add more reserved cooking water if necessary. Add the crushed red pepper and season with salt and pepper. Serve in shallow bowls, sprinkled with the remaining cheese.