In a large saucepan, combine the pork butt, pork liver, water, onions, garlic, bell peppers, celery, 1 teaspoon salt, 1/4 teaspoon cayenne, and 1/4 teaspoon black pepper. Bring the liquid up to a boil and reduce to a simmer. Simmer for 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. Using a meat grinder with a 1/4-inch die, grind the pork mixture. 1/2 cup of the parsley, and 1/2 cup of the green onions, together. Turn the mixture into a mixing bowl. Stir in the rice, remaining salt, cayenne, black pepper, parsley, and green onions. Add the broth, 1/2 cup at a time, and mix thoroughly.