Put Panko in a large bowl, add milk and stir.
Add meat, egg, salt, and pepper to the Panko mixture, and mix very well.
Divide the meat into 4 pieces and roll into oval balls. Push down to form flat steaks.
Heat oil in a frying pan at medium heat. Place the patties in the hot oil, and fry for 4-5 minutes on one side. Flip over and fry for 3-4 minutes covered, until cooked through.
Meanwhile, mix ketchup and Worcestershire sauce in a bowl. Cut melting cheese into thin squares.
Uncover the pan, add sake, then ketchup sauce. Stir and coat the steaks with sauce well. Top with cheese, cover, turn off heat, and let cheese melt for a couple of minutes.