Set up two shallow dishes or pie plates. In one, combine the panko breadcrumbs, parsley, and Parmesan cheese. In the other, beat the eggs with garlic powder, salt, and cayenne until well mixed.
Dip each chicken cutlet into the egg mixture, ensuring both sides are coated. To keep your hands clean, consider using tongs or a fork.
Next, transfer the chicken to the panko mixture, pressing the crumbs onto the chicken to cover it completely. You can either cook the chicken right away or arrange the coated cutlets on a baking sheet, cover, and refrigerate for up to 4 hours.
Heat a large nonstick skillet over medium-high heat. Once hot, add a generous layer of olive oil (start with 2-3 tablespoons). Cook the chicken until golden brown on one side, about 3 minutes. Flip the chicken and cook for an additional 2 minutes. If your skillet isn't large enough for all the cutlets at once, cook in batches, adding more oil as needed.
Transfer the browned chicken to a rimmed baking sheet and bake in the preheated oven for 10 minutes, or until the chicken is fully cooked.
Serve the hot chicken on a platter, topped with arugula or mixed greens. Shave Parmesan cheese over the top using a vegetable peeler, or add more grated cheese if preferred. Squeeze lemon wedges over the chicken and enjoy!