Fill a large pot with lightly salted water and bring to a rolling boil. Stir in spaghetti and return to a boil. Cook pasta uncovered, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Reserve a little pasta water, then drain.

Heat a skillet over medium heat; add guanciale, cook and stir until crisp, 5 to 10 minutes.

Whisk egg yolks and whole egg together in a bowl; whisk in ¾ cup Pecorino-Romano cheese, salt, and pepper until combined.