Step 1

Place the flour in a shallow bowl. Whisk the egg with a small splash of water in another shallow bowl. Place the panko in a deep dish.

Step 2

Lightly pound each cutlet with a meat mallet, then generously season on both sides with salt and pepper.

Step 3

Dredge a cutlet in the flour, coating completely, then shake off any excess. Dip it in the egg mixture, letting any excess drip off, then coat with the panko, gently pressing so the crumbs adhere. Place the breaded cutlet on a plate and repeat with the remaining cutlets.

Step 4

Heat 1/3 inch oil in a medium skillet over medium heat until it shimmers. Add 2 of the cutlets and cook until golden brown, about 3 minutes. Flip and cook until almost cooked through but still pink in the middle, 1 to 2 minutes more. Transfer to a paper towel–lined platter, sprinkle with salt and tent with foil to keep warm. Repeat with the remaining 2 cutlets.

Step 5

Lay the bread on a cutting board in 2 rows of 4 slices. Spread each slice with butter. Squeeze about 1 tablespoon of the tonkatsu sauce over the 4 slices on the bottom row. Top each with some cabbage, then top with a fried pork cutlet. Squeeze about 1 more tablespoon of the tonkatsu sauce over each cutlet. Top each sandwich with the remaining bread.

Step 6

Set a flat platter or tray on top of the sandwiches on the cutting board, then lightly weigh it down with soup cans or similarly heavy items for about 5 minutes. Cut the sandwiches in half on the diagonal, wiping the blade clean between cuts.