Preheat oven to 450°F. Place a wire rack inside a rimmed baking sheet.
On a separate baking sheet, toss panko with 3 tablespoons olive oil. Bake for 3 to 4 minutes until golden brown. Transfer to a shallow bowl.
In a second shallow bowl, beat the eggs.
Pound each pork medallion to 1/4-inch thickness and season with 1/4 teaspoon salt. Dip each piece in egg, letting excess drip off, then press into toasted panko. Transfer to prepared rack.
Roast the breaded pork at 450°F for 10 to 12 minutes, or until golden and cooked through.
Meanwhile, in a medium bowl, mix ketchup, Worcestershire, soy sauce, and 1 tsp vinegar to make tonkatsu sauce.
In a large bowl, whisk honey with remaining 1 Tbsp vinegar and 1 Tbsp olive oil. Add both cabbages and toss well to coat.
Serve pork with slaw and a side of tonkatsu sauce for dipping.