01 - Heat 1 tablespoon olive oil in a large Dutch oven over medium-high heat. Season chicken pieces lightly with salt and pepper. Cook until browned on all sides, approximately 4 minutes. Remove chicken and set aside.
02 - Add sausage to the same pot. Cook, stirring frequently, until browned, about 2 to 3 minutes. Remove sausage and combine with the reserved 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 for an additional 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 if using, and bay leaf. Stir thoroughly to coat the rice evenly with the spices and vegetables.
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 and gently stir. Nestle shrimp into the rice mixture. Cover and cook for an additional 8 to 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 to allow flavors to meld and rice to settle.
09 - Fluff rice with a fork. Garnish with green onions and parsley before serving.