Heat a heavy large pot over medium-high heat for 3 minutes.

Sprinkle the duck pieces with 1 teaspoon of salt and 1/2 teaspoon of pepper.

Sear the duck, skin side down, until golden brown (about 8 minutes per side).

Transfer the duck to a plate using tongs.

Add vegetable oil to the pot, then add flour.

Stir constantly with a wooden spoon until the roux is chocolate-brown (about 25 minutes). If it's still light brown after 20 minutes, increase heat to medium-high for the last 5 minutes.

Add the mushrooms, onion, celery, bell pepper, and garlic to the roux.

Cook until the mushrooms and vegetables are soft, stirring frequently (about 4 minutes).

Add the stout and stir to blend.

Add the chicken broth, Emeril's Original Essence, bay leaves, thyme, cayenne pepper, and the remaining 2 teaspoons of salt.

Stir to blend well.

Return the duck pieces to the pot.

Increase the heat and bring to a boil.

Reduce the heat to medium-low and simmer uncovered until the duck is tender, skimming foam from the surface and stirring occasionally (about 1 1/2 hours).

Transfer the duck to a plate using tongs and let it cool until easy to handle (about 20 minutes).

Remove the meat from the bones; discard the bones and skin.

Cut the meat into 1-inch pieces.

Spoon the fat off the top of the gumbo.

Return the meat to the gumbo; season to taste with salt and pepper.

Cool slightly, then refrigerate uncovered until cold. Cover and keep refrigerated. Bring to simmer before continuing if made ahead.

Divide the cooked white rice among 10 bowls.

Ladle the gumbo over the rice.

Sprinkle with green onions and parsley and serve.