Dry the chicken breasts with paper towels, then use a sharp knife to cut them in half horizontally, creating four filets. If necessary, use a meat mallet to pound each portion to about ½-inch thickness. Season with salt and pepper, to taste.
Preheat the air fryer to 350 degrees F, spraying the inner basket with cooking spray.
In a wide, shallow bowl, whisk together the egg and water until well combined. To a second bowl, add the Panko bread crumbs.
Dredge the chicken in the egg, then press them into the bread crumbs, coating evenly. Repeat the process a second time with each piece, double coating them.
Place the chicken in an even layer in the air fryer basket, spraying the top with cooking spray.
Air fry for 16-18 minutes, carefully flipping the chicken halfway through and spraying with cooking spray before continuing to cook until golden brown and 165 degrees F internally. Repeat with the remaining pieces of chicken.
Transfer the katsu to a cutting board to rest for at least 5 minutes before slicing. Serve over rice, with vegetables and katsu sauce.