Cut the hard rind off the guanciale and discard it. Cut the remaining guanciale into small thick rectangles.

Finely grate the Pecorino Romano cheese. Save a small handful for serving.

Crush or grind the black pepper.

Add the egg yolks and whole egg to a medium mixing bowl. Add most of the grated Pecorino Romano and the black pepper.

Whisk vigorously with a fork or small whisk until the mixture becomes a thick yellow paste. Set it aside.

Add 3 liters of water to a large pot and bring it to a rolling boil. Add the coarse salt.

Add the spaghetti and push it down with tongs as it softens. Cook for 1 minute less than the package instructions for al dente.

While the pasta cooks, place the guanciale in a dry large frying pan over medium-low heat. Do not add oil.

Cook the guanciale for 5–7 minutes until the fat renders and the pieces become crisp and golden. Turn off the heat completely.

Right before the pasta is ready, scoop out about 250 ml of starchy pasta water and set it aside.

Use tongs to move the spaghetti directly into the pan with the guanciale and rendered fat. Toss until the pasta is coated.

Make sure the pan is completely off the heat. Pour the egg and cheese paste over the pasta.

Immediately add about 3 tbsp of the hot pasta water.

Toss vigorously with tongs until the eggs, cheese, guanciale fat, and pasta water form a thick glossy sauce.

If the sauce looks too thick or sticky, add another small splash of hot pasta water and keep tossing until smooth.

Serve immediately with the reserved Pecorino Romano and extra black pepper.