On a cutting board, use a sharp knife to slice each chicken breast lengthwise, so they’re half as thick. Spread cutlets out, then top with a piece of parchment paper. Use a meat mallet or heavy rolling pin to pound the cutlets to an even thickness.
In a small bowl, combine the Kosher salt, parsley, garlic powder, and black pepper. Pat the chicken dry, then brush both sides with some of the olive oil. Use your fingers to sprinkle the seasoning evenly on both sides of the chicken.
Prep three shallow bowls for dipping: one with the flour, one with the eggs, whisked well, and one with the panko.
Dip each chicken cutlet in the flour, coating both sides and shaking off any excess. Then, coat with the egg on both sides. Finally, press each side into the panko crumbs. You can move the chicken back to the cutting board while you dredge the remaining cutlets.
Preheat the oven to 200 degrees and place a cooling rack over a baking sheet.
Heat a large cast iron skillet or heavy pan over medium high heat. Add a tablespoon each of olive oil and vegetable oil to the pan. Heat until it is shimmering, but not smoking, about 375 degrees. Add several chicken cutlets to the pan, without crowding. Cook 2-3 minutes, or until golden brown. Flip, and cook another 2 minutes. The chicken should register at least 160 degrees. Remove the chicken to the cooling rack and place in the oven to keep warm. Repeat with remaining cutlets, adding additional oil as needed.
Sprinkle the finished chicken with flaky salt and sliced fresh herbs, if desired, then serve.