Preheat oven to 500 degrees F. Roughly chop the orange rinds and place in the cleaned duck cavity. Place the stuffed duck on a baking rack over a baking sheet with 1/2-inch of water. Bake until skin turns golden brown and lightly crisps, about 30 minutes. Reduce temperature to 300 degrees and continue cooking until duck reaches an internal temperature of 170 degrees, about 1 hour.

In a medium heavy saucepan combine the orange juice, zest and sugar over medium high heat and reduce to 3/4 cup. Add Peychaud Bitters to orange juice gastrique and set aside.

Add hot duck stock to reduced orange gastrique and simmer over medium low heat for 10 minutes to reduce. Add arrowroot mixture, to thicken.

Remove duck from roasting pan, and discard the fat from pan. Remove orange rinds from duck cavity. Let rest 10 minutes before carving.

Add the Grand Marnier to roasting pan and place over 2 burners on medium high heat. Deglaze pan, scraping continuously with a large wooden spoon. Reduce for 5 to 10 minutes. Pour the orange sauce in the pan into a gravy boat and serve with carved duck.