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. When the bacon begins to crisp up, remove from pan. Add shallot and garlic to bacon fat. Saute for another 2-3 minutes.
Turn off the fire to the skillet.
Drain the pasta into the skillet. Add egg yolk mixture into the pasta and stir constantly. When the pasta sauce has thickened to a creamy and thick consistency, add in crispy bacon, salt, and freshly ground black pepper, and serve immediately. If your sauce is not thickening, turn your skillet on low and mix the pasta constantly until the sauce thickens. Once the sauce thickens, immediately remove pasta from the skillet and serve to prevent curdling of the egg.