Bring a large pot of water to a boil (this dish is salty enough so you don't have to add salt to the water).
While water is coming to a boil, put egg and egg yolk in a large bowl. Whisk together with the pecorino romano and black pepper until well combined. Set aside.
Heat a large nonstick skillet to medium high heat and add guanciale or pancetta. Cook until golden, stirring occasionally, about 4 minutes. Remove from heat.
When water comes to a boil, add gnocchi and cook for 2-4 minutes, just until it floats to the top of the water. With a slotted spoon, scoop gnocchi (it's OK if they're a little wet) into the skillet with the pork and stir to combine. Reserve pasta water.
Add gnocchi and pork mixture to bowl with the egg and cheese and toss gently to combine and let the heat cook the egg and thicken the sauce.
Thin the sauce with reserved pasta water, 1 teaspoon at a time, if desired.
Serve gnocchi with additional cheese and black pepper sprinkled over the top.