Place a heavy-based frying pan (skillet) over a high heat and coat the bottom of the pan with a thin layer of oil.
Put the flour, egg and panko breadcrumbs into three separate bowls. Season the flour with black pepper. Add a little milk to the egg and beat with a fork.
Dip each tuna steak in the flour, making sure it is well coated. Shake off any excess, then dip it in the egg followed by the breadcrumbs.
Place the steaks in the hot oil and cook for one minute on each side.
Meanwhile, finely slice the cabbage with a mandoline or the blade side of a box grater and combine in a bowl with the pickled ginger and pickling juice.
Make the tonkatsu sauce by combining the ketchup, soy sauce, Worcestershire sauce and mirin in a bowl. Grate in the garlic, add the chilli flakes and stir well.
To assemble each sandwich, spread the tonkatsu sauce on two slices of bread and top one of them with the cabbage slaw. Place the tuna steak on the slaw and sit the other slice of bread on top.
Finely slice the apple (if using) using a mandoline or sharp knife, then sprinkle with sesame seeds (if using).
Cut each sandwich in half and serve with the apple salad, lime wedges and any leftover tonkatsu sauce on the side.