Place each chicken breast between two sheets of plastic wrap. Pound it with a meat mallet until it is about ¼ inch thick. Season both sides lightly with salt and pepper.
Pulse 6 to 8 slices of sourdough in a food processor until you get fine crumbs. Any bread works if you do not have sourdough. Stir in the garlic powder.
Line up three shallow bowls. Put the flour in the first, the beaten eggs in the second, and the seasoned breadcrumbs in the third. This setup keeps your hands cleaner and your workflow fast.
Heat your oven to 200°F. Set a wire rack on a baking sheet and keep it nearby. Pour about ¼ inch of oil into a large skillet and heat it over medium-high heat toward 350°F.
Dip each cutlet in the flour first, then in the egg. Press it into the breadcrumbs, coating both sides. Press just enough for the crumbs to stick, then shake off the extra.
Fry two cutlets at a time for about 3 minutes per side, until deep golden. Gently swirl the pan as they cook. The moving oil washes over the coating and puffs it into that classic wavy crust.
Move each finished cutlet to the wire rack in the warm oven. Repeat with the remaining chicken. Squeeze fresh lemon over the top, sprinkle on parsley, and serve right away.