Beat the egg in a shallow dish. Put your desired coating in a separate shallow dish. Season the chicken all over with salt and pepper. Dip in the egg, letting the excess drip off, then firmly press in the coating, making sure to coat both sides.
Heat the vegetable oil in a large nonstick skillet over medium-high heat. Working in two batches, add the chicken and cook until crisp and cooked through, 4 to 5 minutes per side, adjusting the heat as needed if the coating is browning too quickly. Drain on a paper towel–lined plate; season with salt.