Place each pork chop between large sheets of plastic srap and pound iwth a meat mallet, heavy skillet, or rolling pin until 1/2-inch thick. Season both sides with salt and pepper. Place 1½ slices ham on each chop to cover the entire surface, then layer the cheese and piquillos on one half of each chop. Fold each chop in half like a book to enclose the cheese and piquillos. 

Place the flour in a shallow dish, beat the egg in another, and spread the panko in a third. Carefully dredge all the sides of the stuffed pork chops in the flour and shake off the excess. Then, coat in the beaten egg and dredge in the panko. Tap off any excess crumbs.

Add enough oil to a large skillet to come ¼ inch up the sides. Heat over medium-high heat until hot. A pnako crumb should sizzle immediately when dropped in. Add 2 breaded chops and cook, turning once, until golden brown, about 3 minutes per side. drain on paper towels and season lightly with salt. Repeat with the remaining pork chops and serve immediately.