Place fat, gizzards, pork and bay leaves in large heavy skillet over high heat; cook until meat is thoroughly browned, about 6 minutes, stirring occasionally. Stir in the onion, celery, bell pepper, garlic, Tabasco, salt, pepper, paprika, mustard, cumin, thyme, and oregano; stir thoroughly, scraping pan bottom well. Add the butter and stir until melted. Reduce heat to medium and cook about 8 minutes, stirring constantly and scraping pan bottom well. Add the stock and stir until any mixture sticking to the pan bottom comes loose; cook about 8 minutes over high heat, stirring once. Then stir in the livers and cook about 2 minutes. Add the rice and stir thoroughly; cover pan and turn heat to very low; cook about 5 minutes. Remove from heat and leave covered until rice is tender, about 10 minutes. Remove bay leaves and serve immediately.