In your large pot or Dutch oven, heat the olive oil or avocado oil over medium heat. Once hot, add the chopped onion, green bell pepper, and celery. Sauté for about 5 minutes until the vegetables are softened and fragrant. Add the minced garlic and continue to cook for an additional minute.
Add the chopped chicken breasts to the pot. Season with sea salt and Cajun seasoning, adjusting to your taste. Cook for about 5-7 minutes, stirring occasionally, until the chicken is no longer pink.
Stir in the sliced andouille sausage and uncooked brown rice, mixing everything together well. Allow the rice to toast slightly for 2 minutes, absorbing the flavors.
Pour in the chicken broth and diced tomatoes (with their juices). Stir everything together until well combined. Bring the mixture to a boil, then reduce the heat to low. Cover the pot and let it simmer for about 40 minutes, or until the rice is tender and the liquid has been absorbed.
Once the rice is cooked, gently fold in the peeled and deveined shrimp. Cover the pot again and let it cook for an additional 5-7 minutes, until the shrimp are pink and cooked through.
Remove the pot from heat and stir in the chopped fresh parsley. Taste and adjust seasoning, adding more sea salt or Cajun seasoning if desired.