Prepare the ingredients for the sauce by adding the eggs, cheeses and ground pepper into a bowl and whisking until combined. Set aside.
In a medium-sized saucepan, add the diced pancetta or guanciale, and cook over low heat until the fat starts to render and the meat turns crispy, about 5 to 6 minutes.
If you are using bacon, the thickness will determine the length of time it takes to cook. Keep an eye on it, but it should take about 3 to 5 minutes on each side to cook until crispy. If replacing the pancetta with baby spinach, cook with a little olive oil over low heat for about 2 to 3 minutes, until wilted.
While the pancetta is cooking, fill a pot with water and bring it to a boil. Salt the water and add the spaghetti.
Cook the pasta just under the recommended time, as it will continue to cook once you combine all the ingredients together.
Reserve 1 cup (240 milliliters) of pasta water and set it aside, then drain the pasta and add it to the pancetta.
Gently toss the spaghetti with the pancetta and add in some of the reserved pasta water, a little at a time, as this helps deglaze the bottom of the saucepan.
This is very important: You must remove the saucepan from the heat before adding the egg mixture. When eggs hit a very hot pan they immediately start to scramble, which is something you do not want.
Pull the saucepan away from the heat and allow it to cool for 1 or 2 minutes prior to adding the eggs. This will allow the mixture to keep its silky consistency and not curdle.
Pour in the egg mixture a little at a time, while continually stirring the pasta. The residual heat will cook the eggs and create a creamy sauce.
Once all the egg mixture has been incorporated into the pasta, keep on stirring it to reach the desired silky consistency. You can always add extra grated cheese if you feel your sauce is a little runny (in my eyes, adding more cheese is not really a bad thing). The spaghetti should be evenly coated in the silky sauce.
Serve on a platter with another scattering of grated cheese and more freshly ground pepper.