Boil 16 oz (1 lb) gnocchi according to package directions.
While gnocchi is cooking, heat cast iron skillet over medium heat. Add ¼ c chopped meat (pancetta, chopped hard salami, ham) to hot cast iron skillet. Cook until browned, about 3-4 minutes. (if using chopped ham, add 1 teaspoon oil to pan).
While meat and gnocchi are cooking, mix sauce. Crack an egg into a small mixing bowl, grate ⅛ c parmesan cheese into bowl, and add 1 teaspoon lemon juice to egg. Whisk until all incorporated. Set aside.
When gnocchi has been floating for 30 seconds, drain water. Save 1 cup of remaining gnocchi water, and set aside. Add cooked gnocchi to meat in the cast iron skillet. Spread gnocchi out into a single layer on pan. Cook for 2-3 minutes, or until gnocchi is browned on at least one side.
Once one side is crispy and browned, remove from heat then add egg mixture. Mix gnocchi and egg mixture until well incorporated. Add pasta water ¼ cup at a time to thin out the sauce. Return to low heat, simmer until sauce is desired thickness.
Serve immediately, garnish with parmesan cheese and freshly ground black pepper.