Prepare all ingredients before cooking. Finely grate the Pecorino Romano cheese, cut the guanciale into small cubes or strips, and crack the eggs into a mixing bowl. Add the extra egg yolks and set aside.
Bring a large pot of water to a rolling boil. Add salt until the water tastes lightly salty like the sea. Cook the spaghetti according to package instructions until al dente. Reserve about 1/2 cup of pasta cooking water before draining.
While the pasta cooks, place the guanciale in a large frying pan over medium heat. Cook slowly, stirring occasionally, until the fat renders and the meat becomes golden and crisp, about 6 to 8 minutes.
In the bowl with the eggs and yolks, add the grated Pecorino Romano cheese and freshly ground black pepper. Whisk thoroughly until the mixture becomes smooth, thick, and creamy.
Using tongs or a pasta fork, transfer the cooked spaghetti directly into the pan with the guanciale. Allow a little pasta water to come along with the noodles.
Toss the spaghetti with the guanciale over very low heat for about 30 seconds so the pasta becomes coated with the rendered pork fat. Then remove the pan completely from the heat.
Pour the egg and cheese mixture over the hot pasta. Immediately toss and stir continuously with tongs so the heat from the pasta gently cooks the eggs and forms a creamy sauce.
If the sauce is too thick, add a small splash of the reserved pasta water and continue tossing until the sauce becomes smooth, glossy, and evenly coats the spaghetti.
Taste and adjust seasoning if needed. Divide the pasta among bowls and finish with extra Pecorino Romano and freshly cracked black pepper. Serve immediately.