Add the cooled barley and the 1 beaten egg to the potatoes and mix well. Add the salt and pepper and shape the mixture into eight 1/2-inch-thick cakes. Put the flour, the 2 eggs beaten with water and the panko in separate bowls. Dip each cake into the flour, shaking off the excess. Dip the cakes in the eggs, then coat thoroughly with panko crumbs. Redip the cakes in the flour, eggs and panko and set them on a large plate.