In a large saucepan, over medium heat, add the olive oil. Season the duck pieces with salt and pepper. When the oil is hot, sear the duck, fat side down for about 4 to 6 minutes. Turn over the duck and continue to sear for 4 minutes. Remove the duck from the pan and set aside. Add the onions and celery to the pan. Season the vegetables with salt and cayenne. Saute the vegetables until wilted, about 4 minutes. Add the sausage and continue to saute for 4 minutes. Stir in the beans, bay leaves, and garlic. Add the duck stock, water and fresh thyme. Place the duck pieces back into the pan. Bring the liquid to a boil and skim off any cloudy scum that has risen to the service. Reduce the heat to a simmer and cook, uncovered for 3 hours, stirring occasionally or until the meat and beans are tender. Re-season if necessary and stir in the green onions and parsley.
Break and crack the carcass. In a large stockpot, heat the vegetable oil. Season the bones with salt and pepper. Add the bones to the pot and brown for about 10 minutes, stirring often. Add the onions, carrots, celery, garlic, and bay leaves. Season the mixture with salt. Cook until the vegetables are soft, about 5 minutes, stirring often. Add the wine and tomato paste and stir to mix. Cook for 5 minutes, stirring occasionally. Add the water. Put the thyme, parsley sprigs, and peppercorns in a piece of cheesecloth, tie it together with kitchen twine, and add it to the mixture. Bring the mixture to a boil. Skim off any cloudy scum that rises to the surface. Reduce the heat to medium and simmer, uncovered, for 3 hours. Strain through a fine-mesh strainer and cool. Refrigerate overnight and remove any congealed fat from the surface. The stock can be stored in the freezer for 1 month.
Recipe copyright Emeril Lagasse, 1998