Add diced pancetta to a large nonstick skillet over medium heat. Cook, stirring occasionally, until the fat renders & the pancetta becomes golden & crispy, about 5 minutes. Add in the chopped garlic. Cook, stirring constantly to prevent burning, for 1 minute more, until the garlic is slightly softened & very fragrant – your kitchen will smell like heaven! Important: Remove from the heat & set aside.
Meanwhile, as pancetta renders, prep the carbonara sauce egg mixture. Add egg yolks, pecorino & parmesan to a large mixing bowl. Generously season with freshly cracked black pepper. Whisk to combine. The mixture will be thick. Set aside.
Once the pancetta is rendered & the egg mixture is whisked together, cook the gnocchi. Remove the gnocchi from its packaging, using your hands to break apart the individual pieces as needed. Add the gnocchi to the boiling water & cook 3-4 minutes, stirring occasionally to prevent sticking, until the gnocchi float to the top of the pot. Reserve 1 cup of the starchy water, then drain the gnocchi.
Transfer cooked gnocchi to the skillet with the rendered pancetta & garlic. While whisking constantly, pour about ¼ cup of the reserved starchy water into the prepared carbonara sauce egg mixture. The hot water should loosen the egg mixture up quite a bit & begin to melt the cheeses. Transfer the egg mixture to the skillet with the gnocchi, tossing well to combine. Return the skillet to medium-low heat. Continue to toss, adding additional starchy water little by little, until the sauce is glossy & coats the dumplings well. Finish the pasta by tossing in the lemon zest, if using. Remove from the heat.