In a small heavy saucepan heat 2 tablespoons of the oil over medium heat and whisk in flour. Cook, whisking constantly, until roux thickens and darkens to a mahogany color; do not let burn. When well-colored, remove from heat. In a large heavy skillet heat remaining 2 tablespoons oil over medium-high heat and brown ground pork, stirring and breaking up pieces. Add chicken livers, onions, bell pepper and celery and cook, stirring occasionally, until vegetables are tender.
Meanwhile, in a large pot bring gizzards and enough cold water to cover (about 3 cups), to a boil over high heat. Boil until tender, about 30 minutes; drain, reserving stock and gizzards separately. Grind gizzards in food processor and add to pork and vegetable mixture, with roux, reserved stock and Creole seasoning; season to taste with salt and pepper. Bring mixture to a boil, cover and reduce heat to simmering. Cook about 30 minutes, until flavors are well-blended.
Before serving, add parsley, green onions and rice, mixing gently but thoroughly to combine. Adjust seasoning to taste with salt and pepper and serve immediately.
Yield: 4 servings