Bring a large pot of salted water to a rolling boil. Add the spaghetti and cook according to the package directions until it reaches the al dente stage. Crucially, before draining, set aside approximately 1 cup of the starchy pasta cooking water. Drain the pasta and keep it hot.

While the spaghetti is cooking, dice the pancetta or guanciale into small (about 1/4 inch thick) pieces. Heat a large skillet over medium heat and add the diced meat. Cook, stirring occasionally, until the pieces are golden brown and perfectly crispy. Use a slotted spoon to transfer the crispy meat pieces to a paper towel-lined plate, reserving the rendered fat in the skillet.

In a separate bowl, combine the four egg yolks with the majority of the grated Parmigiano Reggiano (save a small amount for serving). Whisk the mixture vigorously until smooth. Season generously with freshly cracked black pepper.

Return the hot, drained pasta directly to the skillet containing the reserved fat and toss it briefly over low heat to coat. Immediately remove the skillet completely from the heat to prevent the eggs from scrambling. Quickly pour the egg and cheese mixture over the pasta, tossing continuously and rapidly to evenly coat all the strands and form a creamy sauce.

If the sauce appears too thick, gradually add the reserved pasta cooking water, a tablespoon at a time, while tossing, until your desired smooth and silky consistency is achieved. Finally, mix in the reserved crispy pancetta or guanciale pieces.