Using a sharp boning or butcher's knife, cut along either side of the backbone, remove and discard. Cut the duck in half through the breastbone. Cut the legs from each half. Remove the first 2 digits of the wings. Set the legs aside and cut the breasts in half horizontally.
Season the duck with 1 teaspoon of salt and the black pepper.
Place a large Dutch oven over medium heat until hot. Place the seasoned duck, skin-side down, in the pan and sear until golden brown, 7 to 8 minutes per side. Remove from the pan.
To the fat remaining in the pan, add the vegetable oil. Stir in the flour. Using a heavy wooden spoon, stir the roux constantly over medium heat until it reaches the color of dark chocolate, 20 to 25 minutes. Add the mushrooms, onions, celery, peppers and garlic and cook, stirring, until soft, 4 to 5 minutes. Add the beer and stir to incorporate. Add the stock, thyme, bay leaves, Essence, cayenne pepper and the remaining 3 teaspoons of salt. Stir well to blend. Increase the heat and bring to a boil. Lower the heat and return the seared duck pieces to the pot. Simmer, stirring occasionally, for 1 hour and 30 minutes.
With tongs, carefully transfer the duck pieces to a platter to cool. When cool enough to handle, remove the skin and discard. Remove the meat from the bones and return to the gumbo. Discard the bay leaves.
To serve, ladle into large soup bowls and top each portion with about 1/4 cup of hot rice. Garnish with the green onions and chopped parsley, and serve immediately.
Combine all ingredients thoroughly and store in an airtight jar or container.
Recipe from "New New Orleans Cooking", by Emeril Lagasse and Jessie Tirsch. Published by William and Morrow, 1993.