Bring a large pot of water to a rolling boil, then add about 1 tablespoon of Salt.
While the water heats, cut the Guanciale into 1/2-inch strips and place them in a cold skillet; cook over medium heat until the fat renders and the pieces are crisp and golden, about 6–8 minutes. Reduce heat if they brown too quickly and keep the rendered fat in the pan.
In a bowl, whisk together the Eggs and Egg yolks until smooth, then stir in about 3/4 cup finely grated Pecorino Romano and a generous grind of Black pepper to make a thick, cheesy custard.
Add the Spaghetti to the boiling water and cook until just al dente according to package directions; before draining, reserve 1 to 1 1/2 cups of the pasta cooking water.
Transfer the drained pasta directly to the skillet with the guanciale over very low heat and toss well so the noodles pick up the rendered fat; remove the pan from the heat.
Working quickly off the heat, pour the egg-and-cheese mixture over the pasta and toss vigorously to create a silky sauce, adding reserved pasta water a few tablespoons at a time until the sauce reaches a smooth, creamy consistency—avoid high heat to prevent the eggs from scrambling.
Taste and adjust seasoning with more Salt only if needed, then serve immediately with extra grated Pecorino Romano and a final crack of Black pepper.
