Pound pork chops or chicken breasts to about 1/2 inch thickness using a meat mallet or heavy skillet. Season both sides generously with salt and pepper.

Set up a breading station: flour in the first shallow bowl, beaten egg in the second, and panko in the third. Dredge each cutlet in flour and shake off excess, dip fully in beaten egg, then press firmly into panko to coat all surfaces. Let rest for 5 minutes before frying.

Pour vegetable oil into a large heavy skillet to a depth of about 1/2 inch. Heat over medium heat until the oil reaches 350 degrees F. Test by dropping a small pinch of panko into the oil. It should sizzle immediately and turn golden within 30 seconds.

Fry each cutlet for 3 to 4 minutes per side until deep golden brown and cooked through to an internal temperature of 165 degrees F for chicken or 145 degrees F for pork. Fry in batches to avoid crowding the pan. Transfer to a wire rack or paper towel-lined plate to drain.

While the cutlets drain, combine ketchup, Worcestershire sauce, soy sauce, mirin, brown sugar, and Dijon mustard in a small saucepan. Stir over low heat for 2 to 3 minutes until the sugar dissolves and the sauce thickens slightly.

Slice each katsu cutlet into strips across the grain. Divide cooked rice among 4 bowls, add a layer of shredded cabbage, then arrange the sliced katsu on top. Drizzle generously with tonkatsu sauce and add optional toppings. Serve immediately.