Bring a pot of water to a boil and add the spaghetti. Cook spaghetti for 6 – 8 minutes or until al dente (cooked so as to be still firm when bitten). While the water is boiling, cook the bacon pieces in a large skillet over medium-high heat until the bacon is crispy. Do not drain off the bacon fat. Keep warm.
Whisk the egg yolks with the cream and half the cheese. When the pasta is done, add about 2 or 3 tablespoons of the hot pasta water to the egg mixture and whisk. Drain the spaghetti and add it to the skillet with the bacon. Stir the spaghetti so that it absorbs the bacon flavor. With the skillet off the heat, pour the egg mixture into the skillet and stir quickly. Serve immediately with the remaining Parmesan on the side.