In a baking dish, rub the birds with the cider vinegar. In a small bowl, combine the coarse salt and brown sugar. Rub the pheasants with the salt mixture. Cover and refrigerate for 4 to 24 hours.
With the rack in the middle position, preheat the oven to 400 °F (200 °C).
Drain and pat the pheasants dry. In a large roasting pan, toss the squash, potatoes, shallots, garlic and bacon with the oil. Place the birds over the vegetables. Bake for about 1 hour and 30 minutes or until a meat thermometer inserted into the thigh without touching the bone reads 180 °F (82 °C).
Meanwhile, in a saucepan, bring the brown sugar, vinegar, garlic and pepper to a boil. Continue cooking until the sauce has caramelized, about 2 minutes. Add the broth and apple juice. Simmer over medium heat for about 45 minutes or until the sauce has reduced by half.
Dissolve the cornstarch in the water. Drizzle the cornstarch mixture in the sauce, whisking constantly. Simmer for 2 minutes.
You can replace the pheasants with guinea fowls or quails. The baking time will vary according to the size of the game.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.