Bring a large pot of salted water to a boil for the spaghetti.
In a medium bowl, whisk together the eggs and egg yolks. Stir in the freshly grated Pecorino Romano cheese and set aside.
Cut the guanciale into small cubes or lardons. Add to a non-stick skillet over medium heat and cook for 7–10 minutes until crispy and the fat has rendered. Do not drain the fat.
Cook the spaghetti until al dente, about 7 minutes. Reserve ½–1 cup of pasta water before transferring the pasta.
Using tongs, transfer the spaghetti directly into the skillet with the guanciale. Toss well so the pasta absorbs the rendered fat.
Remove the skillet from direct heat and quickly stir in the egg and cheese mixture. Toss continuously until the sauce becomes creamy. Add reserved pasta water a little at a time if needed.
Season generously with freshly ground black pepper and additional salt if desired. Serve immediately with extra Pecorino Romano or Parmigiano-Reggiano on top.