The next day, preheat the oven to 250 degrees F.
Place the ducks in the oven and slowly roast until the meat is tender and moist, about 5 hours. Two hours into the cooking, use the pastry brush to brush another 1/4 cup of the glaze over the ducks. After an additional 2 hours, brush the remainder of the glaze over the ducks. Remove the ducks, allow to cool for 20 minutes, and use kitchen shears to remove the backs from the ducks, and a chef's knife to cut through the breast bone and around the rib cage.
Season the duck legs with the kosher salt and pepper and place them in a small baking dish. Add the carrot, celery, onion, duck fat, and coffee. If the duck legs are not completely submerged, add enough vegetable oil to cover. Cover the baking dish tightly with aluminum foil and bake, undisturbed, until meat is fall-from-the-bones tender, 6 to 7 hours.
Yield: about 2 cups confit duck meat