To make the brining liquid, in a large, heavy pot combine the water, salt, peppercorns, and chile flakes, and bring to a boil. Remove from the heat and submerge in an ice bath until cool. Add the ducks and weight with a small plate to submerge in the brine. Refrigerate at least 24 hours and up to 48 hours, turning occasionally to ensure that the ducks are evenly brined.

Remove the ducks from the brine. Bring a large pot of water to a rolling boil. Add the ducks, 1 at a time, and poach for 3 minutes each. Remove with tongs and place on a wire rack set over a baking sheet. Pat dry with paper towels. Pour 1/4 cup of the glaze onto the topside of each duck, rubbing to coat evenly. Refrigerate uncovered for 24 hours, spreading an additional 1/4 cup of glaze on each duck 3 times.

Preheat the oven to 500 degrees F.

Remove the ducks from the refrigerator and let come to room temperature, 20 to 30 minutes. Spread about 1/2 cup of glaze over each duck, rubbing to coat evenly. Roast until deep golden brown, 15 to 18 minutes. Lower the temperature to 375 degrees F and roast until the skin is a deep mahogany color and the juices run clear, 1 hour and 45 minutes to 2 hours. Add 1 cup of water every 30 minutes to the bottom of the roasting pan to prevent the dripping glaze from burning. Remove from the oven and let rest for 15 minutes before carving.

With poultry sheers, cut along either side of the backbone and remove. With a sharp knife, cut through the breastplate and remove the rib cage. Drizzle with additional glaze, if desired, and serve one duck half per person.

Combine all the ingredients in a large, heavy saucepan and bring to a boil. Reduce the heat to medium low and simmer until the sauce is reduced by half to a thick syrup, about 1 hour and 15 minutes. Remove from the heat, discard the cinnamon stick, and let cool before using.

Saute the shallot in butter until translucent, about 3 minutes. Add the haricots verts and saute until firm but cooked. Season with salt and pepper, to taste. Toss with the parsley.