Using a vegetable peeler, make long ribbons of the cucumber and carrot. Place the cucumber in a colander and toss with salt. Allow to drain for 10 minutes.
In a small bowl, whisk vinegar, sugar, soy sauce and sesame oil. Place carrot and cucumbers into the bowl and combine well. Cover and refrigerate.
Katsu Sauce
In a saucepan, combine the chicken broth, onions, soy sauce, mirin, ginger, garlic, brown sugar, 1 tsp. sesame oil and red pepper flakes.
Bring to a boil, then lower the heat and simmer, uncovered, while you cook the chicken.
Stove Top Instructions for Chicken
Line up 3 shallow bowls. In the first shallow bowl, combine the flour, kosher salt and pepper. Beat the eggs and water in the second bowl. In the third bowl, place the panko bread crumbs.
Fill a large frying pan with 1/2 inch of vegetable oil and heat to medium. Pound the chicken breast thin using a meat mallet. Alternatively, slice each breast crosswise so you create 2 very thin cutlets. Dredge chicken in the flour mixture, then the egg, then the panko.
Fry until chicken is golden brown and easily pierced with a fork, about 9-10 minutes on each side. (Chicken should always reach an internal temperature of 165 degrees). Remove chicken onto a paper towel-lined plate. Slice into strips.
Air Fryer Instructions for Chicken
Preheat air fryer to 350 degrees.
Line up 3 shallow bowls. In the first bowl, combine the flour, kosher salt and pepper. Put the beaten egg and water in the second bowl. In the third bowl, place the panko bread crumbs.
Place the chicken into the air fryer and make sure they are not touching each other. (You may have to do it in batches). Coat the tops of the chicken generously with nonstick cooking spray. Air fry for 9 minutes.
Flip the chicken over. Coat generously with nonstick cooking spray. Air fry for an additional 8 minutes. Extend the time by 2-3 minutes for larger pieces of chicken. Slice chicken into strips.
Assemble the Bowls
Heat the sesame seeds over medium-low heat in a small frying pan. Constantly moving them around, toast the seeds until they start to brown slightly and become fragrant. Remove from heat and set aside.
Divide the cooked rice among four bowls. Pour katsu sauce over the rice, then top with chicken strips, pickled vegetables, diced green onion and toasted sesame seeds.