Put the hen, water, quartered onions, celery pieces, bay leaves, 1 tablespoon of the salt, and 1 teaspoon of the cayenne in a large, heavy pot. Bring to a boil over high heat, then reduce the heat to medium and cook, partially covered, until the hen is tender, about 2 hours. Remove the hen, strain the broth, allow it to cool and reserve.  Makes about 3 quarts.

In a large, heavy pot or a Dutch oven over medium heat, combine the oil and flour. Stirring slowly and constantly, make a dark brown roux, the color of chocolate, 20 to 25 minutes. Add the chopped onions, bell peppers, chopped celery, garlic, and chopped sausage. Cook, stirring, until the vegetables are very soft, 8 to 10 minutes. Add the remaining 1 1/2 teaspoons salt and the remaining 1/2 teaspoon cayenne.  Add the reserved broth and stir until the roux mixture and broth are well combined. Bring to a boil, then reduce the heat to medium-low and cook, uncovered, stirring occasionally, for 1 1/2 hours.

Meanwhile, remove the skin from the hen and pick the meat off the bones, discarding the skin and bones. Coarsely chop the chicken meat. Add the chicken and the sliced sausage to the gumbo. Cook for 15 minutes. Remove from the heat and let sit for 5 minutes before skimming off the fat that has risen to the surface.

Stir in the green onions and parsley and serve the gumbo in individual soup or gumbo bowls.