Score the duck skin by making diagonal shallow cuts all over at half-inch intervals. Repeat going the opposite direction.
Heat a non-stick frying pan. Lay the duck on the pan, skin side down. Cook over high heat until lightly browned.
Transfer the duck to a plate. Pour off the duck fat.
Return the frying pan to the stove with the heat set to medium. Pour in the soy sauce, mirin and sake. Stir in the honey (if using) and grated ginger.
Put the duck breast pan in the pan, skin side up. Cover the pan and cook the duck over low heat for 15 to 20 minutes or just until done.
Transfer the duck to a chopping board. Cut into slices about half an inch thick.
Place rice on a plate. Arrange the duck on top. Drizzle in the pan juices. Sprinkle with sliced scallions and toasted sesame seeds.