Slice the cabbage as thinly as possible, close to the thickness of fettuccine noodles.
Whisk together eggs, parmesan, pecorino if using, and black pepper. Set aside at room temperature.
Cook diced pancetta in a dry skillet over medium heat for 6 to 8 minutes, until crisp, rendering its fat.
Add sliced cabbage and garlic to the pan. Cook 6 to 8 minutes, stirring frequently, until softened.
If excess liquid pools in the pan, let it reduce for a minute or two uncovered.
Remove pan from heat completely, let sit 30 seconds, then pour in egg mixture, tossing constantly with tongs.
If the sauce is too thick, add a splash of reserved pan liquid, tossing constantly, until glossy.
Serve immediately, topped with extra cheese and black pepper.