In a large, deep pot combine the wines, soy sauces, and water. Bring to a boil over high heat and add the duck. If the liquid doesn't cover the duck, add more water. Bring to a boil again, then reduce the heat and simmer, skimming the liquid until no more scum forms, about 30 minutes.
Add the rock sugar, ginger, garlic, long scallion pieces, star anise, chiles, and cinnamon sticks. Stir to dissolve the sugar and taste the liquid for sweetness. It should be pleasantly sweet; if not sweet enough, add more sugar. Place a second pot or stainless steel bowl half-filled with water into the first to keep the duck submerged (see Tips) and simmer until the duck is very tender and almost falling from the bones 2 ½ to 3 hours. Do not overcook or the meat will come apart. One hour into cooking, add the lotus. During the last 10 minutes of cooking, add the bok choy.
Using a large-mesh spoon, carefully remove the duck and bok choy to a platter and cover with foil to keep warm. Strain and skim the stock, return it to the pot, and reduce it over high heat until lightly syrupy, about 20 minutes.
Transfer the duck to a serving platter and surround it with the bok choy and lotus. Glaze the duck with the sauce, garnish it with the scallion greens, and serve.
Beverage tip: spicy, dried-cherry shiraz/syrah ustralian (brokenwhood hermitage).