Preheat oven to 350°F (175°C).
Melt duck fat in a large casserole dish over medium heat.
Place all remaining ingredients in casserole dish, cover, and place in oven.
Bake for 2 hours 30 minutes or until meat falls off the bone.
Let cool to room temperature for 30 minutes.
Remove meat from cooking fat, then strain liquid and set aside. Set aside 1/2 cup of duck fat for rillettes topping.
Debone duck meat and remove skin.
In a large bowl, shred meat with a fork.
Pour fat over meat while stirring. Mixture will blanch slightly.
Portion out into pretty jars or ramekins and top with reserved duck fat.