When liquid returns to a boil, dip the duck into liquid and spoon liquid over duck. Repeat until duck is thoroughly moistened. Repeat dunking once more. Hang duck by the string in a cool airy place with a bowl underneath to catch drips. Leave for 4 to 6 hours until skin is dry and taught. Put roasting pan on lower oven rack and fill with 2 to 3 inches of water. Oil the upper rack above pan.
Preheat oven to 350 degrees F.
Remove the chopstick and string. Put duck on oiled rack in center of oven breast side up and cook for 30 minutes. Turn duck breast side down for 45 minutes, then turn breast side up for 30 minutes or until skin is dark brown. While duck is roasting, make scallion brushes. Trim roots, and cut off most of green part, leaving 3-inch pieces. Make several 1-inch lengthwise slits in each end of scallion, and put in a bowl of ice water for 20 minutes, drain and refrigerate. Mix hoisin with sesame oil and 1 tablespoon water, in a small serving bowl. Carve the duck, separate meat and skin. Place on a serving platter and surround with the scallion brushes. Serve the sauce with the duck.