With the rack in the middle position, preheat the oven to 180 °C (350 °F).
Place the duck in a large pot and cover with water. Bring to a boil. Reduce the heat and simmer for 30 minutes.
Drain and return the duck to the pot. Add the wine, duck stock, onion, garlic, thyme, and bay leaf. Season with salt and pepper. Bake for about 2 hours and 30 minutes or until a meat thermometer reads 82 °C (180 °F).
Remove the duck from the pan and let cool. Strain the cooking juices through a sieve. Discard the garlic, onion and herbs. Allow the fat to come the surface of pan juices and skim. You’ll need 375 ml (1 1/2 cups) of skimmed pan juices.
Debone the duck and cut the meat into small pieces. Set aside.
Half an hour before the end of cooking, cook the potatoes in salted boiling water. Drain well and mash with the cheese, butter, milk, egg, and parsley. Season with salt and pepper. Keep warm.
In a saucepan, sauté the onion in the butter. Add the duck and its pan juices. Adjust seasoning.
Pour the duck mixture in a 33 x 23-cm (13 x 9-inch) baking dish or in six 13-cm (5-inch) ramekins. Cover with the mashed potatoes. Sprinkle with breadcrumbs and Parmesan cheese. Bake for 15 minutes, then brown under the broiler. Sprinkle with chopped chives and serve.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.