Combine the egg yolks (reserving the whites for another use), cream, parmesan cheese and salt and pepper. Let stand at least one hour, until room temperature. Do not skip this step!
Start the water for the pasta, adding the tbsp of salt when it boils. Meanwhile, in a large non-stick skillet with high sides, fry the bacon pieces until crisp. Remove the bacon from the pan to a paper towel, and drain all but 1 tbsp of the fat. The water for the pasta should come to the boil at about this point, so add the spaghetti noodles. Reduce the heat, stir, and cook about 7 minutes or until al dente. Drain, reserving 1 cup of the pasta-water.
Add the diced onion to the pan with the reserved bacon fat, and saute over medium-high heat until slightly colored, about four minutes. Add the minced garlic and saute a further minute.
Add the drained spaghetti to the pan with the onions and garlic. Remove immediately from the heat and add the egg yolk mixture. Stir one minute, the residual heat will "cook" the sauce. Do not return the pan to the burner, it will scramble the egg yolks. Check the creaminess of the dish, if needed, add a few tbsp at a time of the reserved pasta-water until desired creaminess is attained. Return the bacon crumbles to the dish, stir.
Using tongs, twist up portions of the Carbonara to plate. Garnish with the fresh chopped parsley and extra parmesan cheese. Serve and enjoy!