Remove the skin from the legs; discard the skin. Cut the meat from the bones, reserving meat. Trim the excess fat from the duck carcasses. Using a meat cleaver, chop carcasses into small pieces. (This exposes the marrow of the bones, allowing it to enrich the sauce.)
Place the bone pieces in a shallow baking pan. Roast in a 500 degree F oven for 20 to 30 minutes or until quite brown, but not burned. Turn the bones, once in a while, to ensure an even browning.
While the bones are roasting, cut the leg meat into small pieces. In an 8-quart Dutch oven, heat olive oil over medium-high heat. Add the meat pieces and cook until done and quite brown; drain off the excess oil.
Peel the vegetables. Cut the vegetables into medium pieces. Add the vegetables, herbs, and spices to the meat. Add the cognac. Bring to boiling. Deglaze the pan, making sure to scrape up all the bits of brown from the bottom of the pot. Add the 1 cup of dry wine and the muscat wine. Return to boiling. Boil for 10 minutes.
Add the bones and the chicken broth. Return to boiling. Reduce the heat and simmer, uncovered, for 4 hours, skimming off any scum that has appeared on the surface of the sauce. Set a fine wire sieve over a bowl. Pour the hot broth through the sieve. Discard vegetables, bones, and seasonings. Using a large metal spoon, skim off the fat that rises to the top. Measure the amount of stock. Cover and refrigerate stock for at least 6 hours. Then use a spoon to lift off the fat that solidifies on the surface of the stock.
In a medium saucepan, add duck stock. (A broad low-sided heavy saucepan works the best for reducing liquids, but any size will do.) Bring to boiling. Boil until the stock is 1/3 the original amount. (This will make a medium-bodied sauce. The sauce can be reduced still further if a more intense flavor is desired.) Season to taste with salt and the 2 tablespoons of wine. (The wine brightens the flavor of the sauce.)