Preheat the oven to 400 degrees F.
For the beans: In a large saucepan, melt the butter. Saute the onions and celery for 3 to 4 minutes, or until they are slightly wilted. Add the beans, salt, cayenne, water and bay leaf and bring to a boil. Reduce heat to medium low and cook until beans are tender and most of the water is absorbed, about 2 hours.
For the meats: In a large oven proof skillet, over medium high heat, combine the flour and oil. Stirring constantly, make a medium brown roux. Add the onions, celery, bell peppers, carrots, salt and cayenne. Stirring constantly, cook for 3 to 4 minutes or until vegetables are slightly wilted. Add the duck legs and sausages and cook for 2 to 3 minutes on each side. Add the chicken broth and stir the mixture until the roux and broth are combined and mixture thickens. Scrape the bottom and sides of the pot to loosen any brown particles. Bring to a boil. Add the beans and duck meat. Reduce the heat to medium low and cook for 30 minutes.
For the Gratine: In a mixing bowl, combine the bread crumbs, cheese, parsley, Essence, and olive oil. Mix well. When the bean meat mixture is cooked, spoon the grantine evenly over the top and bake for 10 minutes or until lightly browned. Spoon a serving of the mixture from the pan onto a plate and garnish with Essence, shaved chives and crusty bread.
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.