Gather the ingredients.
In a large saucepan over high heat, bring the chicken or beef broth to a boil.
Add the chicken gizzards to the broth and reduce heat to low; simmer the gizzards for 30 minutes.
Remove with a slotted spoon and grind them or chop them very finely. Reserve the broth.
Add the drippings or oil and 2 tablespoons of the butter to a Dutch oven or flameproof casserole over medium heat. When the oil and butter mixture is hot, add the ground pork and ground or chopped gizzards.
Cook, stirring frequently until browned.
Lower the heat. Add the onions, celery, bell pepper, garlic, salt, pepper, paprika, and cayenne. Stir and continue cooking until the vegetables are tender—about 5 to 7 minutes.
Add the rice and reserved broth and then quickly bring to a boil. Preheat the oven to 250 F.
Stir, cover, and reduce the heat to low. Simmer for 15 minutes, or until the rice is tender.
Sauté minced chicken livers in the remaining 2 tablespoons of butter for 3 minutes.
Toss the minced chicken livers with the rice, taste for seasoning, and adjust with more salt and pepper, as needed.
Cover the pan or casserole and place it in the preheated oven for 10 minutes.
Fluff with a fork.
Serve and enjoy.