Pat the pork cutlets dry. If they are not pre-pounded, place each one between two sheets of plastic wrap and pound with a meat mallet or the bottom of a small skillet until an even half inch thick. Season both sides with the salt and pepper.
Set up a dredging station: flour in one shallow bowl, beaten eggs in a second, panko in a third. Working one cutlet at a time, coat in flour and shake off the excess, dip in egg, then press firmly into the panko so the crumbs stick on both sides.
Preheat the air fryer to 400°F (200°C) for 3 minutes. Spray the basket lightly with oil, then arrange the cutlets in a single layer without overlapping, working in batches if your basket is small.
Spray the tops of the cutlets with oil. Air fry for 6 minutes, flip, spray the second side, and cook for another 5 to 7 minutes, until deep golden brown and the internal temperature reads 145°F (63°C).
While the cutlets cook, whisk together the ketchup, Worcestershire sauce, oyster sauce and brown sugar for the tonkatsu sauce, or skip this step if using store-bought sauce.
Let the cutlets rest for 3 minutes before slicing into strips. Resting keeps the juices in the meat instead of on the cutting board.
Serve sliced over rice with the shredded cabbage alongside, sauce drizzled over the top or served on the side for dipping.