If using chicken breast, cut the chicken breast in half, butterflying into 2 thin cutlets.

Place the butterflied cutlets or the whole thighs, one at a time, in a heavy-duty zipper-lock bag and pound gently to ¼-inch thickness using a meat pounder or the bottom of a heavy 8-inch skillet. Season generously with salt and pepper. Let sit at room temperature for 15 minutes, or for best results, refrigerate for at least 4 hours and up to overnight after seasoning.

Set a (6-quart) air fryer to 350°F (175°C) and preheat for 5 minutes. Place flour, beaten eggs, and panko in three separate shallow bowls. Add oil to the panko and stir until the panko is well-coated. Working with one cutlet at a time, dredge in flour, shaking off excess. Dip chicken in egg, then dredge in panko, pressing gently to help panko adhere; transfer chicken to a plate. Repeat the process with the remaining cutlet.

Place the prepared cutlets into the preheated air-fryer basket. Spray the tops of the chicken with cooking spray. Cook until golden-brown, 6 to 8 minutes, then flip the chicken cutlets and spray the top of the cutlets with cooking spray. Cook until golden brown and internal temperature reaches 155°F (68℃), 6 to 8 minutes for breasts and 175℉ (80℃) for thighs. Transfer chicken to a cutting board. Sprinkle with additional salt to taste and let rest for 5 minutes.

Slice katsu into thin strips. Serve with tonkatsu sauce, cabbage, and white rice, if using.