Combine the Panko breadcrumbs Parmesan cheese, Italian seasoning, and garlic powder together. Place this mixture in a shallow bowl.
Place the flour in a shallow bowl, and the beaten eggs in another shallow bowl.
Season each chicken breast with salt and pepper on both sides.
Dredge each chicken breast first in the flour, shaking off any excess. Then dip into the eggs.
Then dip the chicken into the breadcrumb mixture. You may have to press the mixture to adhere.
Dip the chicken back into the eggs and then breadcrumbs once more.
Transfer the chicken breast to a parchment lined baking sheet.
Repeat the process with the other 3 thin chicken breasts.
Heat 1 tablespoon of butter with 3 tablespoons of vegetable oil in a large cast iron skillet (or a heavy oven-proof frying pan).
Add all four pieces of chicken and cook for a few minutes on each side or until browned on each side. The chicken should not cook all the way through on top of the stove. It will finish cooking in the oven.
Place the cast iron skillet in a preheated 400°F oven and continue to cook until they reach an internal temperature of 165°F. (If the chicken cutlets are thin, they shouldn't take long at all to finish cooking in the oven.)
Remove from the oven and serve immediately.
Notes
*Alternatively use 2 thick boneless chicken breasts each sliced in half lengthwise (so now there is 4 chicken breasts) and then pounded thin.