01 - Heat 1 tablespoon olive oil in a large Dutch oven or heavy pot over medium-high heat. Season chicken pieces lightly with salt and pepper. Cook until browned on all sides, about 4 minutes. Remove chicken and set aside.
02 - Add sausage to the pot and cook, stirring constantly, until browned, about 2–3 minutes. Remove and set aside with the chicken.
03 - Add remaining 1 tablespoon olive oil to the pot. Sauté onion, bell pepper, and celery for 5 minutes until softened. Add garlic and cook another minute until fragrant.
04 - Stir in tomato paste, then add diced tomatoes with their juices. Cook for 2 minutes, scraping any browned bits from the bottom of the pot to incorporate the fond.
05 - Add rice, smoked paprika, Cajun seasoning, thyme, oregano, cayenne, and bay leaf. Stir thoroughly to coat the rice evenly with spices.
06 - Return chicken and sausage to the pot. Pour in chicken broth. Bring to a boil, then reduce heat to low. Cover and simmer for 20 minutes, stirring occasionally to prevent sticking.
07 - Uncover pot and gently stir. Nestle shrimp into the rice mixture. Cover and cook for an additional 8–10 minutes, until rice is tender and shrimp are pink and cooked through.
08 - Remove from heat. Discard bay leaf. Let stand, covered, for 5 minutes. Fluff rice with a fork and garnish with green onions and parsley before serving.