Cut the chicken breast into smaller pieces, and pound them to uniform thickness. Season the pounded chicken fillets with salt, pepper, and cayenne pepper on both sides.
Dust the chicken fillets with flour on both sides. Beat eggs. Soak the chicken fillets into the egg batter and leave them there until they're ready to pan fry.
Heat a pan skillet with a good amount of vegetable oil on medium heat. Dip one egg-saturated chicken fillet into the panko on both sides, and then place onto the skillet to pan fry. Repeat with the other fillets. Flip until one side is golden brown. Pan fry each side for about 4-5 minutes, or until inside is completely cooked. The chicken katsu is done at this point. Keep the egg batter from the chicken katsu for the side dish.
With the same skillet, turn the heat to low, and add a dial of oil. Pour the egg batter into the skillet. When the egg coagulates, roll it up with a spatula and serve.
Pair the chicken with katsu sauce. Top the egg roll with bonito flakes and and mayonnaise.