In a bowl, whisk together eggs, egg yolks, Pecorino Romano, Parmesan, and black pepper.
Add drained spaghetti to the skillet with the rendered fat. Toss to coat.
Remove skillet from heat. Quickly pour egg and cheese mixture over the pasta, tossing continuously to coat. The residual heat will cook the eggs into a creamy sauce.
Add reserved pasta water, a tablespoon at a time, as needed to achieve a silky, emulsified sauce.
Season with salt if necessary. Serve immediately, garnished with extra cheese and pepper.
Notes
For a creamier sauce, ensure your pasta water is hot when you add it to the egg mixture.
Using guanciale provides a more authentic flavor, but pancetta is a good substitute.
The key to avoiding scrambled eggs is to toss the pasta off the heat and use the residual heat from the pasta and skillet.
The ratio of eggs to cheese can be adjusted to your preference.