Bring a large pot of water to a rolling boil over high heat, then add the kosher salt. While waiting for the water to boil, whisk together the egg yolks, whole egg, and grated Pecorino Romano cheese in a medium bowl until a thick, smooth paste forms.

Heat a large skillet over medium-low heat and add the cubed guanciale. Cook for 6 to 8 minutes, stirring occasionally, until the fat has rendered completely and the pork is crispy and golden brown, then remove the pan from the heat.

Drop the spaghetti into the boiling water and cook for about 8 to 9 minutes, or until it is slightly firmer than al dente. Just before draining, carefully scoop out and reserve 1 cup of the starchy pasta cooking water.

Transfer the drained spaghetti directly into the skillet with the crispy guanciale and rendered fat. Toss the pasta over low heat for 30 seconds to allow the noodles to absorb the savory pork flavor.

Remove the skillet from the heat entirely to prevent the eggs from scrambling. Slowly whisk 1/4 cup of the reserved hot pasta water into the egg and cheese mixture to temper it, then pour the mixture over the warm spaghetti.

Toss and stir the pasta vigorously for 1 to 2 minutes, adding a splash more pasta water if needed, until a glossy, creamy sauce wraps around every noodle. Divide among warm bowls, garnish with a generous amount of freshly cracked black pepper and extra Pecorino Romano, and serve immediately.