Combine all brine ingredients in a plastic container with a lid. Place the lid on the container and shake to dissolve the salt.
Remove the pop-up thermometer, liver, gizzards, and heart. Cut off the wings.
Using kitchen shears, locate the spine at the base of the neck. Cut up the line of the backbone towards the neck cavity. Turn the duck and cut straight towards the rear cavity. Remove the backbone.
Turn the duck over and cut straight down the middle of the breast bone, leaving 2 equal duck halves. To separate the legs from the breast, flip your halves over so the flesh side is facing up at you. Using a knife, make a crescent shape cut between the leg and the breast. Lay your knife flat against the skin and make 3 marks in one direction and then in the other, making an X. Make sure that you are cutting through the skin and not the meat.
Line the inside of a plastic lexan or a pot with a zip-top bag. Place the duck quarters inside the bag, and pour the brine over the duck. Seal the bag, ensuring that all air is removed from the bag. Brine the duck for 2 to 2 1/2 hours in the refrigerator.
Bring 1 1/2 inches to 2 inches of water to a boil in a large pot. Place a colander into the pot and line the sides of the colander with the duck. Do not stack the duck quarters on each other. Cover and turn the heat to medium low. Steam the duck for 45 minutes. Set oven to 475 degrees F. Place a large cast iron skillet into the oven.
Remove duck pieces from steamer and place legs, skin side down, into the hot skillet. Place the skillet into the hot oven immediately and cook the leg quarters for 10 minutes. Add the breasts, skin side down, and cook for 7 more minutes or until the duck takes on a deep mahogany color and the skin is very crisp.
Remove the duck from the skillet and rest under foil. Add the chard and the shallots to the skillet. Toss the chard in the fat until it barely wilts. Season with the sherry or balsamic vinegar.
Serve the duck with the chard.