Preheat your oven to 200°F to keep the chicken warm after cooking.
Slice the chicken breasts in half horizontally to create thinner cutlets. Place them between two sheets of plastic wrap and gently pound them to an even thickness of about 1/2 inch.
In three shallow dishes, set up your breading station: in the first dish, add the flour; in the second dish, whisk the eggs; and in the third dish, combine the Parmesan cheese, garlic powder, salt, and black pepper.
Dredge each chicken cutlet in the flour, shaking off the excess, then dip it into the egg, and finally coat it with the Parmesan mixture, pressing gently to adhere.
In a large skillet, melt 1/4 cup of butter over medium heat. Once hot, add the chicken cutlets in batches (do not overcrowd the pan) and cook for about 4-5 minutes on each side, or until golden brown and cooked through. Transfer the cooked cutlets to a baking sheet and keep them warm in the oven.
In the same skillet, add the remaining 1/4 cup of butter, lemon juice, and lemon zest. Stir to combine and let it simmer for 1-2 minutes.
Remove the chicken from the oven and drizzle the lemon butter sauce over the cutlets. Garnish with chopped parsley before serving.