With the rack in the middle position, preheat the oven to 180°C (350°F).
In a roasting pan over medium-high heat, brown the shanks in the oil and butter, in batches if necessary to avoid crowding the pan. Season with salt and pepper.
Deglaze the pan with the brandy and vinegar. Reduce by half.
Add the honey and broth and bring to a boil. Season with salt and pepper. Return the shanks to the pan. Add the orange, onion and garlic. Roast for 1 hour, basting the shanks regularly. Place the remaining vegetables around the shanks, making sure they are sitting in the broth. Season with salt and pepper. Continue roasting for about 45 minutes or until the shanks are nicely glazed. Cover and cook for 30 to 45 minutes more or until the vegetables are tender and the meat is falling off the bone. If necessary, strain the pan juices and reduce over high heat.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.