It is important to immediately add the egg mixture to the hot pasta in step 5. The hot pasta cooks the eggs, which thickens them and creates a luscious, creamy sauce that coats the pasta. We call for Pecorino Romano here, but Parmesan can be used, if preferred. If guanciale is difficult to find, you can substitute pancetta; just be sure to buy a 4-ounce chunk and not presliced pancetta. It's best to use freshly ground black pepper here.
Bring 4 quarts water to boil in large Dutch oven.
Meanwhile, beat eggs and yolks, Pecorino, pepper, and salt together in bowl; set aside. Combine guanciale and oil in 12-inch nonstick skillet and cook over medium heat, stirring frequently, until guanciale begins to brown and is just shy of crisp, about 6 minutes. Remove skillet from heat.
Add pasta and 1 tablespoon salt to boiling water and cook, stirring often, until al dente.
Reserve ½ cup cooking water, then drain pasta and immediately return it to pot. Add guanciale and rendered fat from skillet and toss with tongs to coat pasta.
Working quickly, whisk ¼ cup reserved cooking water into egg mixture, then add egg mixture to pasta in pot. Toss pasta until sauce begins to thicken and looks creamy, 1 to 2 minutes. Adjust consistency with remaining reserved cooking water as needed. Serve immediately, passing extra Pecorino and pepper separately.
