Heat oil in a large heavy pot or Dutch oven.
Brown the diced pork on all sides and set aside.
Add andouille sausage slices to the pot and cook until browned; set aside with the pork.
Sauté onion, bell peppers, and celery until softened.
Add garlic, tomato paste, Cajun seasoning, smoked paprika, thyme, pepper, and salt.
Stir in the rice and toast lightly.
Add tomatoes and chicken broth, mixing well.
Return pork and sausage to the pot; add bay leaf.
Bring to a boil, reduce heat, cover, and simmer for 25–30 minutes.
Remove bay leaf, fluff with a fork, and garnish.