Bring a large pot of water to boil. Boil pasta according to package directions (approximately 7-10 minutes).
Make egg yolk mixture by mixing together salt, egg yolks, heavy whipping cream, and Parmigiano Reggiano.
Heat skillet on medium high and place bacon in the pan. Cook for about 10-15 minutes. When there is enough fat released for the bacon to cook in its own fat, turn the fire to medium low to allow bacon to render and become crispy. When the bacon begins to crisp up, remove from pan.
Place bacon onto paper towels to absorb excess fat. Pour out 95% of the bacon fat into a bowl and set aside to discard after it cools. Add shallot and garlic to the remaining bacon fat in the pan. Saute for another 2-3 minutes.
Turn off the fire to the skillet.
When the pasta is al dente or has just a bite, drain the pasta into the skillet. Add egg yolk mixture into the pasta and stir constantly. Turn the fire on the lowest setting to help the sauce cook and thicken, about 1-2 minutes.
When the pasta sauce has thickened to a creamy and thick consistency, remove from the pan to stop the cooking. Add freshly ground black pepper, season with salt to taste, top with bacon, and serve immediately. Add extra grated Parmigiano Regianno to taste.
