Heat a tablespoon of the duck fat from the confit in a nonstick frying pan over medium heat.
Add the diced celery, carrot, and shallot and cook until the vegetables begin to color.
Then add the chopped duck and sauté for a minute or two.
Add the breadcrumbs and cream and cook a few moments pulling it all together.
Transfer the mixture to a plate and divide evenly in two.
Place the frying pan back on the heat.
Preheat the oven to 200°F.
Butter two 2.75- or 3-inch rings.
Place the rings in the frying pan and fill each with the hash mixture, pressing it down to form a cake.
Cook for 4-5 minutes until golden brown then, using a spatula, flip the cake and the ring, pressing the cakes back down inside the ring to make contact with the pan.
When then are golden on the bottom, transfer the cakes with their rings to serving plates, carefully remove rings, and place plates in the oven to keep them warm.