Lightly pound the pork chops until thin. Season generously with salt and pepper. Dip in flour, then the egg, then the panko to bread.
Heat up 2 inches of oil in a deep, heavy bottomed pan over medium heat. When it reaches 350°F, carefully drop in the pork chops, being sure not to crowd the pan and cook, flipping once, until golden and cooked through, about 4-6 minutes per side, depending on thickness. Drain on paper towels or a wire rack.
Whisk together the vegetable oil, rice vinegar, and sesame oil. Taste and season with salt and pepper. Toss with the shredded cabbage, adjusting to taste.
Make the burger: spread on mayo and mustard on the bottom bun and top with a tonkatsu cutlet and a generous amount of cabbage. Drizzle on tonkatsu sauce to taste. Enjoy!
