With the rack in the middle position, preheat the oven to 180°C (350°F).
In a large ovenproof skillet or Dutch oven over medium-high heat, brown the duck legs skin side down. Turn over the legs. Spoon any excess fat from the skillet if desired. Season with salt and pepper. Add the onions and garlic and cook until browned. Add the wine, carrot and bay leaf. Bring to a boil. Cover, transfer to the oven and bake for 1 1/2 hours. Uncover and bake until the flesh pulls easily from the bone, about 30 minutes to 1 hour more.
Remove the duck from the skillet. Discard the carrot and bay leaf. Let cool. Debone the duck. Set aside.
Reduce the cooking liquid until thick. Add the duck and green onions. Adjust the seasoning. Set aside and keep warm.
Boil the potatoes and garlic in salted water until the potatoes are tender, about 15 minutes. Drain.
Using a ricer or masher, mash the potatoes and garlic with the butter. Add the milk and cheese and purée using an electric mixer. Adjust the seasoning.
With the rack in the middle position, preheat the broiler.
Spoon the duck mixture into four 180-ml (3/4-cup) ramekins. Top with mashed potatoes. Place a wedge of cheese on each portion.
Broil until the cheese melts and browns lightly.
Serve with a green salad or green beans.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.