Fill a large pot about 3/4 of the way with water and put it on high heat. When the water boils, add the pasta and cook until al dente as marked on the package. Do not drain the pasta!
While waiting for the water to boil, cut the bacon into small squares about 1/2 inch on each side; heat the olive oil in a large saute pan on medium-low heat and add the bacon. Cook the bacon until the fat renders out and it begins to crisp, then turn off the heat.
While the bacon is cooking, beat together the eggs and egg yolk; add the grated cheese and mix until combined. Add black pepper to taste.
Once the bacon and the pasta are cooked, transfer the pasta directly from its pot into the saute pan. Mix so that the pasta is coated in bacon fat; if not all the pasta is shiny, then add butter or olive oil a teaspoon at a time until the pasta is completely coated. Turn the heat back on and cook together for 3-4 minutes or until the pasta-bacon mixture is warm and steaming, then turn off the heat.
Add the egg-cheese mixture to the pan, stirring vigorously and tossing the pasta in the pan as you do so. If the sauce seems too thick, add pasta water from the pot a teaspoon at a time until the desired consistency is reached; if the sauce is too thin, add grated cheese. Taste and add salt and pepper as desired, and serve immediately.