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In a large 6 quart Dutch oven heat about 2 teaspoons of the oil over medium-high heat. Working in four batches, start by adding half of the chicken and browning it until golden on both sides. Remove chicken with a slotted spoon to a medium-sized bowl. Add another teaspoon of oil repeat this process with the remaining chicken. In two more batches repeat the process with the sausage pieces until all the meats are browned. Cover the bowl with foil wrap and set aside.
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In the same Dutch oven over medium-high heat, add the remaining oil and sauté onion, garlic, celery, green, red and yellow bell peppers while stirring, until just tender, about 2 minutes. Add the rice and stir to coat, about 1 minute. Add chicken broth, tomatoes and season with bay leaf, paprika, oregano, thyme, salt, pepper and hot sauce as desired. Stir well to combine.
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Return browned chicken and sausage along with any accumulated juices to the Dutch oven. Over medium-high heat, bring the mixture to a light boil while stirring. Cover and let boil for 5 minutes. Reduce heat to low, keep covered and cook for 30 minutes, stirring occasionally until the rice is tender and all the liquid has been absorbed.
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Meanwhile, thaw shrimp in a large bowl of cold water for about 30 - 45 minutes. Once thawed, remove the shells and tails and discard them. Add shrimp to the Dutch oven and gently stir to combine and immerse the shrimp. Cook on low for 10 - 15 minutes until the shrimp is pink and cooked through.