Pour the olive oil into a large 5-quart Dutch oven or heavy-bottomed pot and heat over medium-high flame. Lightly season the chicken pieces with Cajun seasoning and sear them in the hot oil for about 3–5 minutes until the surfaces are golden. The chicken should remain slightly pink inside at this stage. Remove and set aside on a plate.
Next, add the sausage slices to the same pot. Allow them to brown for roughly 5 minutes, releasing their flavorful oils. Stir in the onion, bell pepper, and celery mix, scraping the browned bits from the bottom of the pan to capture every bit of flavor. Cover and let the vegetables cook for 5 minutes, stirring once midway through to ensure even softness.
Return the browned chicken to the pot and pour in the diced tomatoes and chicken broth. Sprinkle in the parsley, basil, garlic powder, Cajun seasoning, salt, and pepper. Mix thoroughly and taste the broth, adjusting seasoning as needed.
Add the uncooked rice and stir until evenly combined. Bring the mixture to a gentle boil, then cover and lower the heat to the lowest simmer. Allow it to cook for 10 minutes before uncovering to stir once, gently folding the rice from the bottom to the top.
Replace the lid and continue simmering for another 30 minutes without lifting the cover. Keep the heat low and steady—a soft simmer ensures tender rice and balanced flavor. Avoid boiling or stirring too frequently.
When the rice is fully tender and has absorbed the rich, seasoned broth, the jambalaya is ready. If the rice still feels slightly firm, pour in about ½ cup of additional broth, stir gently, cover again, and cook for 5–10 more minutes.