Combine the chopped bacon and the butter in a heavy skillet over medium heat. Sauté until the bacon begins to get crisp. Use a slotted spoon to transfer the bacon to paper towels.
Whisk the cream, the grated Parmesan, and the egg yolks in a medium bowl just to blend. Whisk in two tablespoons of drippings from the skillet. Set the cream mixture aside and discard the remaining drippings.
Cook the pasta in a pot of boiling salted water until it is just tender. Stir occasionally to keep it from sticking to the bottom of the pan. Drain the pasta and return it to the same large pot that it cooked in.
Add the cream mixture and toss over medium low heat until the sauce cooks through. The pasta should be coated thickly. Mix in the bacon. Season to taste with the salt and pepper.
Pass the additional cheese separately.