Step 1Cook the spaghetti in rapidly boiling salted water over high heat until it is just tender but with a needle-thin core of crisp.
Step 2While the spaghetti is cooking, heat the guanciale and oil in a skillet over medium heat just until the guanciale begins to brown and crisp, 2 to 3 minutes. Remove the pan from the heat, but keep it warm.
Step 3Break the eggs into a small bowl and add all of the cheese and a generous grinding of pepper. Whisk gently until smooth.
Step 4Drain the cooked pasta (reserving and keeping warm a cup of its water) and put it in the skillet with the guanciale over low heat. If it sizzles loudly, the pan is too hot; let it cool slightly. Toss quickly to mix well and coat the spaghetti with the rendered fat.
Step 5Holding the skillet slightly above but not touching the burner, pour the egg and cheese mixture in a stream into the pasta. Toss the pasta or stir it quickly with spoons to coat the spaghetti in a creamy sauce made from the lightly cooked eggs. Work quickly so the spaghetti does not get cold, or the eggs will stay raw and runny. But don’t let the pan get too hot or the eggs will curdle. If either starts to happen, you can rescue it by stirring in a little of the reserved warm cooking water.
Step 6Taste and add more salt and pepper if desired before serving immediately.