Preheat oven to 200 F. Line a large rimmed baking sheet with a wire rack. 

To make the Pork Milanese: One at a time, place pork between two 1-gallon plastic storage bags. Using a flat meat pounder or a rolling pin, pound the pork until wider and about 1/3 inch thick. Spread flour in a shallow, wide bowl. Beat eggs in a second bowl and spread bread crumbs in a third bowl. Coat pork chop in flour, shaking off excess, dip in eggs and then coat with bread crumbs. Place on another baking sheet and let stand 5 minutes to set coating. 

Pour enough oil into skillet to come about 1/8 inch up sides of pan and heat over moderately high heat until oil shimmers. In two batches without crowding, add pork and cook, adjusting heat so pork does not burn, until underside is golden brown, 2 to 3 minutes. Flip pork and cook until other side is golden brown, 2 to 3 minutes more. Transfer to wire rack and keep warm in oven while cooking remaining pork. 

Meanwhile, make the cacio e pepper: Bring a large pot of salted water to a boil over high heat.When second batch of pork is in skillet, add spaghetti to water and cook according to package directions. Scoop out, reserve 1/3 cup of cooking water, discard the rest. Drain spaghetti and return to pot. Add Parmesan and Romano cheeses and pepper. Mix well, adding enough of the cooking water to make a creamy sauce. 

Transfer pork and pasta to dinner plates. Sprinkle with parsley and serve hot with lemon wedges.