Boiling a large pot of salted water. Once boiling, add the spaghetti and cook it according to the package's instructions until it reaches al dente texture. Before draining, reserve about 1 cup of the pasta cooking water for later use, then drain the pasta and set it aside.
While the pasta is cooking, cut the pancetta or guanciale into small, 1/4 inch thick pieces. Heat a large skillet over medium heat, and add the diced meat. Cook, stirring occasionally, until the pieces are nicely crispy and golden. Remove the crispy pieces from the skillet with a slotted spoon, setting them aside on a paper towel-lined plate. Keep the rendered fat in the skillet.
In a bowl, separate the egg yolks from the whites (the whites can be saved for another recipe or discarded). Add the majority of the freshly grated cheese to the yolks (reserve a small amount for serving), and whisk them together vigorously. Season this mixture with a generous amount of freshly cracked black pepper.
Transfer the drained, still-hot pasta directly into the skillet with the rendered fat over low heat. Toss the pasta to ensure it's thoroughly coated in the fat.
Remove the skillet from the heat to prevent the eggs from scrambling in the next step. Quickly pour the egg and cheese mixture over the pasta, tossing continuously to coat the pasta strands evenly and create a smooth, creamy sauce.
If the sauce appears too thick, gradually add the reserved pasta cooking water until you reach your desired consistency. Finally, add the crispy pancetta (or guanciale) pieces back into the skillet and toss everything together once more.
Dish out the carbonara immediately after mixing, garnishing each serving with the remaining grated cheese and an extra sprinkle of black pepper to taste.
