Bring a large pot of generously salted water to boil for the pasta.
In a medium bowl, whisk together egg yolks, whole eggs, and grated Pecorino Romano. Set aside.
Heat olive oil in a large skillet over medium heat. Add guanciale and crushed garlic (if using). Cook until the fat has rendered and the meat is crispy, about 5-7 minutes. Remove garlic cloves.
Cook fettuccine in the boiling water according to package instructions until al dente.
Reserve 1½ cups of pasta cooking water before draining.
Working quickly, add the hot pasta to the skillet with the guanciale. Toss to coat with the rendered fat.
Remove the pan from heat and let it cool for 30 seconds (this prevents scrambling the eggs).
Pour the egg mixture over the pasta, tossing vigorously with tongs. Add reserved pasta water, a little at a time, until the sauce becomes creamy and coats the pasta.
Season generously with freshly ground black pepper and serve immediately with extra cheese.