Roasting the Carcass: Preheat your oven to 400°F (about 200°C). Place the duck carcass on a baking sheet and roast for 30-40 minutes, until browned. This step enhances the flavor of the broth.
Combining Ingredients for Broth: Transfer the roasted duck carcass to a large stockpot. Add water and rendered duck fat to the pot.
Simmering: Bring the mixture to a boil, then reduce the heat to a low simmer. Allow the broth to simmer gently for 6-8 hours. Skim off any foam or impurities that rise to the top during the first few hours of simmering.
Seasoning: Add salt to the broth in the last hour of cooking, adjusting to taste.
Straining the Broth: After simmering, remove the pot from the heat. Strain the broth through a fine-mesh sieve into a large container, discarding the duck carcass and any other solids.
Cooling and Storing: Allow the broth to cool to room temperature before storing. Refrigerate for up to 5 days or freeze for longer storage. A layer of fat will solidify on the top when chilled, which can be removed if desired, or left to enrich the broth.