Place the turkey in a 15-quart (15 litre) pail or stainless steel pot. Keep chilled.
In a large pot, bring 2 cups (500 ml) of the water, the brown sugar, salt, cinnamon and pepper to a boil. Stir until the sugar and salt have dissolved. Add a little of the cold water to cool the mixture. Pour over the turkey. Add the remaining cold water to cover the turkey. Refrigerate for 48 hours.
With the rack in the lowest position, preheat the oven to 325°F (165°C).
In a bowl, combine the pork, bacon, apples, breadcrumbs and cinnamon. Season with salt and pepper. Keep chilled.
Remove the turkey from the brine. Pat dry.
Gently work your fingers under the skin of the breast and legs, loosening it without tearing. Spread the applesauce evenly under the skin.
Fill the turkey cavity with the stuffing. Tie the drumsticks together with butcher’s twine to help the turkey keep its shape. Brush the turkey with butter and cover the breast with the moistened cheesecloth.
Scatter the carrots and celery on the bottom of a large roasting pan and pour in the chicken broth. Place the turkey on the vegetables and surround it with the onions. Drizzle the vinegar over the onions. Season with salt and pepper. Roast for 2 ½ hours.
Remove the cheesecloth and continue cooking until a meat thermometer inserted in the thigh without touching the bone reads 180°F (82°C), 1 hour 15 minutes. If necessary, add broth so there is always about 2 cups (500 ml) of liquid in the bottom of the roasting pan. If any parts of the turkey begin to scorch during cooking, cover them with foil.
Remove the onions and keep warm. Transfer the turkey to a serving platter. Cover and let rest for 20 minutes. Strain the liquid from the roasting pan into a sauceboat and spoon off any fat. Adjust the seasoning.
Serve the turkey with the onions, mashed potatoes and the roasting juices.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.