In a shallow bowl, mix flour, Parmesan, salt, pepper, paprika and garlic powder.
Cut each chicken breast into 3 pieces, place between two sheets of plastic wrap, and pound to 1/4-inch thickness. Rub chicken with 1 tablespoon olive oil (divided between both sides). Coat evenly in the flour mixture.
Heat 2 tablespoons olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add half the chicken pieces and cook for 3–4 minutes on one side until golden brown. Flip and cook for 1–2 minutes on the other side.
Transfer cooked chicken to a plate, sprinkle lightly with salt, and cover with foil to keep warm. Cook remaining chicken, adding more oil if needed.