Wipe duck inside and out with a damp cloth. Peel potatoes and cut in thick slices. (Keep in cold water until ready to use.)
Heat oil in a large heavy pan. Brown duck quickly on all sides. Drain off excess fat. Tie or sew up duck's neck to seal. Place bird tail-side up in a deep bowl.
Crush garlic. Cut leeks in 2-inch sections. In one cup mash red bean cheese with brown bean sauce and salt. In another, combine sugar, soy sauce, sherry and star anise.
Heat remaining oil and brown garlic lightly. Add red bean cheese mixture and cook, stirring over medium heat, to blend and heat through.
Add water, leek sections and sugar-soy mixture. Continue stirring to blend and heat.
Pour 1 to 2 cups of this sauce mixture into duck cavity. Add remaining star anise. Sew up cavity securely or skewer so that liquid cannot leak out.
Leave remaining sauce mixture in pan and bring to a boil. Add duck and potato slices and simmer, covered, 20 minutes. Turn bird over and simmer, covered, 20 minutes more.
Remove duck, leaving liquids in pan. Let bird cool slightly; then chop, bones and all, in 2-inch sections. Shred lettuce and arrange on a serving platter with duck and potato slices on top.
Reheat liquids in pan. Meanwhile blend cornstarch and remaining cold water to a paste, then stir in to thicken liquids. Pour over duck and potatoes. Garnish with Chinese parsley.Servings: 8