Bring a large pot of water to a rolling boil and add the coarse salt.

While the water heats, prepare the carbonara base. In a medium bowl, whisk together the 2 whole eggs, 2 egg yolks, 1 cup of grated Pecorino Romano, and 1 teaspoon of freshly cracked black pepper until smooth and well combined. Set aside.

Place the diced pancetta in a large, cold skillet. Turn the heat to medium and cook, stirring occasionally, for 7-10 minutes, or until the fat has rendered and the pancetta is golden brown and crispy. Turn off the heat and leave the pancetta and its rendered fat in the skillet.

Drop the gnocchi into the boiling water. Cook according to package directions, typically for 2-3 minutes, or until they float to the surface. Do not overcook.

Just before the gnocchi are done, scoop out about 1 cup of the starchy cooking water and set it aside. Using a slotted spoon, transfer the cooked gnocchi directly from the pot into the skillet with the pancetta and rendered fat. Gently toss to coat the gnocchi.

IMPORTANT: Let the skillet with gnocchi and pancetta cool for about 1 minute. This is crucial to prevent the eggs from scrambling. Add a splash (about 1/4 cup) of the reserved starchy water to the skillet and stir to combine. This will cool the pan slightly and help create a creamy sauce.

Slowly pour the egg and cheese mixture over the gnocchi while continuously and vigorously tossing or stirring everything together. The residual heat from the gnocchi and the skillet will cook the eggs into a silky, creamy sauce. Continue tossing for about 1-2 minutes until the sauce thickens and clings to the gnocchi.

If the sauce is too thick, add another splash of the reserved starchy water until you reach your desired consistency. Taste and adjust seasoning if necessary, though it likely won't need salt.

Serve immediately in warm bowls, garnished with an extra sprinkle of Pecorino Romano cheese and a generous amount of freshly cracked black pepper.