Bring a large pot of salted water to a boil. Add the spaghetti and cook until al dente, reserving about 1 cup of the pasta water before draining.
While the pasta cooks, cut the guanciale into small strips or cubes. Heat a pan over medium heat and cook the guanciale until crispy and golden. Remove from heat and set aside, keeping the fat in the pan.
In a bowl, whisk together the egg yolks, whole egg, grated cheese, and a generous amount of black pepper until smooth and creamy.
Add the drained hot pasta to the pan with the guanciale and its fat. Toss well to coat.
Remove the pan from the heat (important to avoid scrambling the eggs), then quickly add the egg and cheese mixture, tossing rapidly to create a creamy sauce. Add reserved pasta water a little at a time if needed to loosen the sauce.
Serve immediately with extra Pecorino and freshly ground black pepper on top.