In a large sauce pan, 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 both 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 and liver together with 1/2 cup of the parsley and 1/2 cup of the green onions. Turn the mixture into a large 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. Taste and adjust the seasoning if necessary – depending on how salty the cooked rice is, you may or may not need additional seasoning. The mixture should be moist enough to hold together when you press it between your fingers but should not be overly wet.