Using a meat mallet, rolling pin, or heavy skillet, pound the chicken to a ¼-inch thickness and season all over with 1 teaspoon salt and ½ teaspoon pepper. Sprinkle the flour over the chicken and turn to coat, shaking off any excess.

In a shallow bowl, whisk the eggs until blended and season with a pinch each salt and pepper. In another shallow bowl, combine the breadcrumbs, cheese, garlic powder, and ½ teaspoon pepper. Dip each cutlet in the egg mixture, allowing the excess egg to drip off, then add to the breadcrumb mixture, pressing so the crumbs adhere.

In a large heavy skillet, add ¼ inch of oil. Heat over medium-high until the oil is shimmering. Working in batches to avoid crowding, add cutlets to the skillet and cook until golden brown and just cooked through, 2 to 3 minutes per side. Reduce the heat if the chicken is browning too quickly. The chicken is done when it registers 165°F in the thickest part and is opaque and no longer pink when you slice into the center.