Put the pork, liver, water, onions, bell peppers, celery, 1 teaspoon of the salt, 1/4 teaspoon of the cayenne, and 1/4 teaspoon of the black pepper in a large heavy pot. Bring to a boil over high heat. Reduce the heat and simmer for about 1 1/2 hours, or until the pork and liver are tender. Remove from the heat and drain, reserving 1 1/2 cups of the broth.
Grind the pork and liver together with 1/2 cup of the parsley and 1/2 cup of the green onions in a meat grinder fitted with a 1/4-inch die. Or, put the pork and liver together with 1/2 cup of the parsley and 1/4 cup of the green onions in a food processor fitted with a metal blade and pulse several times to coarsely grind the mixture. It should not be pureed into a paste.
Transfer to a large mixing bowl. Add the rice, the remaining salt, cayenne, black pepper, parsley, and green onions and mix well. Add the broth, 1/2 cup at a time, and mix thoroughly.
Either stuff the mixture into 1 1/2-inch-diameter casings and make 3-inch links or form it into balls the size of walnuts.
Serve warm. The sausage can be reheated in a 325ºF. oven.
Yield: about 4 1/2 pounds