1. Heat oil in a high-sided pan over medium-high heat. Cook and stir pork until well browned and fat is rendered, 5 to 7 minutes. Add onion, celery, and bell pepper; saute until translucent, about 5 minutes. Stir in paprika, cumin, black pepper, cayenne, garlic powder, oregano, and thyme. Cook, stirring occasionally, until vegetables continue to soften, about 5 minutes.
2. Reduce heat to medium and add andouille sausage. Cook and stir to release some flavor, 2 to 3 minutes. Stir in chicken livers and rice until well coated. Season with salt, pour in broth, and bring to a simmer over medium-high heat. Add bay leaf and Worcestershire sauce. Cover tightly; reduce heat to medium-low. Cook, without stirring, until most of the liquid is absorbed and rice is starting to get tender, about 25 minutes.
3. Add green onions and parsley; mix well. Continue cooking over low to medium-low heat until rice is tender, about 10 minutes more. Taste for seasoning and remove bay leaf before serving.