In the bowl of a food processor, combine the mushrooms, andouille, onions and garlic. Pulse until the mixture forms a coarse paste, about 10 times. In a large saute pan, heat 1 tablespoon of the olive oil. When the oil is hot, add the mushroom mixture. Season the mixture with Essence, salt and pepper. Saute for 4 minutes. Stir in the port and cook for 1 minute. Remove the pan from the heat and stir in the bread crumbs and cool completely. Season each quail, inside and out with the remaining olive oil and Essence. Stuff each quail with 1/4 cup of the duxelles and wrap the skin around the stuffing. Make an incision in the bony end of one leg of each bird and insert the other leg through the incision to keep the legs crossed to make a nice presentation. Place the quail on a parchment-lined baking sheet, about 1 inch apart. Place the baking sheet in the oven and roast the quail until they're golden brown and crisp-skinned, for about 20 minutes.
Serve the quails with the sauce ladled over the top.
Heat the oil in a large saucepan over high heat. When the oil is hot add the shallots and garlic. Season with salt and pepper. Saute for 1 minute. Stir in the sugar and port, bring to a boil, and cook for 3 minutes. Stir in the stock and cook over high heat, for about 20 minutes. Remove from the heat and serve hot.
Combine all ingredients thoroughly.