Heat the olive oil in a large deep skillet over medium-high heat. Add the cubed chicken and sliced sausage. Sprinkle with one tablespoon of the Cajun seasoning. Sauté for 5-6 minutes until the chicken is golden brown and the sausage has developed a nice crust. Remove the meat from the pan and set it aside on a plate; it does not need to be cooked through completely yet.

In the same skillet, add the onion, bell pepper, and celery. If the pan looks dry, add a tiny splash of broth. Cook for 4-5 minutes until the vegetables soften. Stir in the minced garlic and the remaining tablespoon of Cajun seasoning, cooking for just one more minute until the garlic becomes fragrant.

Add the rinsed rice to the skillet and stir it around for a minute to toast the grains slightly. Pour in the chicken broth and scrape the bottom of the pan to release any browned bits. Return the chicken and sausage to the skillet. Bring the liquid to a boil, then immediately reduce the heat to low. Cover the skillet with a tight-fitting lid and simmer for 15-18 minutes, or until the liquid is absorbed and the rice is tender.

Remove the skillet from the heat but keep the lid on. Let it sit undisturbed for 5 minutes; this allows the rice to finish steaming perfectly. Remove the lid, fluff the mixture with a fork, and top with fresh parsley and green onions. Serve hot.