Slice each chicken breast in half horizontally and pound the thicker ends to 1/4 inch thick. Cut the bigger pieces in half; you want to end up with sandwich-size pieces.
Beat the eggs in a medium bowl. Stir in the parsley, garlic, salt, and pepper. Sprinkle one side of the chicken pieces with salt and slip them into the beaten eggs. Mix with your hands to coat. The chicken can be cooked right away, or let marinate in the refrigerator up to overnight.
Sprinkle some panko on a small rimmed baking sheet. Put a piece of chicken on top,and cover with more panko. Then, with your fist, pound the panko into the chicken to adhere. Pound slowly at first, and then a little harder, until the crumbs stick.
Pour 1/4 inch of oil (about 1 cup) into a 10-inch nonstick skillet and heat over medium to medium-high heat. It’s ready when a sprinkle of panko sizzles. Fry 1 to 2 cutlets at a time, without crowding, flipping only once, until nicely browned, about 3 minutes on the first side and 1 minute on the second. Transfer to a tray lined with paper towels.