Combine the salt, pineapple-orange juice, peppercorns, thyme, and garlic 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 from the duck. Cut off the wings with a knife or kitchen shears.
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 and reserve for another use, like stock.
Turn the duck over and cut straight down the middle of the breastbone, leaving 2 equal duck halves. To separate the legs from the breast, flip your halves over so the flesh side is facing up. 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 just the skin and not the meat.
Line the inside of a food-safe plastic container or pot with a zip-top bag. Place the duck quarters inside the bag, and pour the brine over the duck. Seal the bag, removing as much air as possible. Brine the duck for 2 to 2 1/2 hours in the refrigerator.
When ready to cook, place a 12-inch cast iron skillet in the oven and heat oven to 475ºF. Meanwhile, bring 1 1/2 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 to render out some of the fat.
Remove the duck pieces from the steamer (Save the water for another use, like cooking potatoes.) and place the legs, skin-side down, into the hot skillet. Return the skillet to the hot oven immediately and roast the leg quarters for 10 minutes. Add the breasts, skin-side down, and cook until the duck takes on a deep mahogany color and the skin is very crisp, about 7 more minutes.
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.