Place the chicken breasts on a cutting board. Use a sharp knife to slice the chicken breast halves horizontally, butterflying them open. Cut each breast in half, to create 4 equal size pieces. Cover the chicken with plastic wrap. Use a mallet or rolling pin to pound the chicken out until it is about 1/4-inch thick. Remove the plastic wrap and season with salt and pepper.
In a medium shallow bowl or baking dish, combine the flour, garlic powder, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Set aside.
In a separate medium bowl or baking dish, whisk the eggs and set aside.
In a third medium shallow bowl or baking dish, combine the panko, Parmesan cheese, parsley, and lemon zest.
Dredge the chicken breasts in the flour mixture, coating both sides, shaking off excess. Next, dip the chicken into the eggs, letting any excess drain off. Add the chicken to the panko mixture and press until both sides are well coated. Repeat until all pieces are all breaded.
In a large cast iron skillet, heat the oil over medium high heat. Once the oil is hot, carefully place 1 or 2 pieces of chicken into the pan and cook for 2 to 3 minutes, on each side, or until chicken is cooked through.
Remove the chicken to a paper towel lined plate and repeat the process with the remaining chicken. Add more oil, if necessary.
Transfer chicken to a plates and serve with arugula salad and lemon wedges for squeezing.