Season the rabbit with 1 teaspoon of the Essence. Heat 1 tablespoon of the oil in a heavy skillet over medium-high heat. Add the rabbit and cook until golden, about 3 minutes per side. Transfer the rabbit to a large platter.
Add the andouille to the pan. Cook, stirring, until browned, about 10 minutes. Using a slotted spoon, transfer the andouille to the rabbit platter. Add more oil to the pan if needed, then add the mushrooms and cook, stirring until soft, about 5 minutes. Transfer to the platter.
Whisk the remaining 1 1/2 cups oil and the flour in a large heavy pot or Dutch oven until smooth. Cook over medium-high heat, stirring constantly with a wooden spoon, to make a dark chocolate-colored roux, 25 to 30 minutes.
Add the onions, celery, and bell peppers and cook, stirring often, until the vegetables soften, about 5 minutes. Add the garlic and stir until fragrant, about 1 minute. Add the Worcestershire and hot pepper sauces and stir well. Carefully add the beer (it will splatter), and stir well to blend. Stir in the stock and bay leaves. Add the rabbit, andouille, and mushrooms and bring to a boil. Reduce the heat to medium-low and simmer, uncovered, until the rabbit is tender, about 45 minutes.
With tongs or a long-handled spoon, transfer the rabbit pieces to a large platter and let cool slightly.
Add the remaining 2 tablespoons Essence and the salt to the gumbo and simmer over medium-low heat, stirring occasionally, for another hour.
Meanwhile, remove the rabbit meat from the bones, discarding the bones, and cut into bite-size pieces. During the last 5 minutes of cooking, stir the rabbit into the gumbo. Just before serving, remove the bay leaves.
To serve, spoon the gumbo into soup bowls and add a big spoonful of the rice to each.
Yield: 12 servings