Bring a large pot of water to a rolling boil. Once boiling, season the water with salt and add the pasta. Cook until the noodles are al dente according to package instructions. Before draining, scoop out half a cup of the starchy water and set aside. Drain the pasta thoroughly.

In a wide sauté pan set over medium heat, render the chopped bacon until it turns crisp and golden. Once cooked, switch off the heat, leaving the bacon and its rendered fat in the pan.

In a separate mixing bowl, whisk together the two whole eggs, two additional yolks, finely grated cheese, and freshly ground pepper until the mixture becomes smooth and homogenous.

With the heat still off, transfer the drained hot pasta into the skillet with the cooked bacon. Immediately pour in the egg-and-cheese mixture, and quickly toss everything together using tongs or a large spoon. The residual heat from the pasta will gently cook the eggs, forming a silky sauce. Add the reserved pasta water a little at a time to achieve the desired creamy consistency.

Serve the dish right away, garnished with extra grated cheese and a light dusting of black pepper if preferred.