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Cut the guanciale into strips or small cubes. Place it in a cold frying pan and heat over medium-low heat until golden and crisp, about 8–10 minutes. Transfer the guanciale to a plate, leaving the rendered fat in the pan.
Bring a large saucepan of water to the boil. Add a good pinch of coarse salt and cook the spaghetti until al dente, following the packet instructions. Reserve a mugful of the pasta water (about 120 ml), then drain the spaghetti.
Meanwhile, in a large bowl, whisk together the egg yolks and whole egg. Stir in the Pecorino Romano and a generous grind of black pepper to form a smooth paste. If the mixture is too thick, loosen it with a teaspoon of the reserved pasta water.
Return the drained spaghetti to the pan with the fat and remove it from the heat. Pour over the egg and cheese mixture and toss vigorously, adding one or two tablespoons of the reserved pasta water at a time until the sauce is creamy and coats the pasta.
Stir in half of the crispy guanciale, then divide the pasta between warm plates. Top with the remaining guanciale, extra grated Pecorino Romano and a final grind of black pepper. Serve immediately.