Heat the olive oil in a large Dutch oven or heavy pot over medium-high heat. Season the chicken pieces with a pinch of salt, pepper, and 1 teaspoon of the Cajun seasoning. Add the chicken to the hot pot in a single layer. Let it cook without moving for 3 to 4 minutes, until deeply golden brown. Flip the pieces and cook for another 2 to 3 minutes. Transfer the seared chicken to a plate and set aside.

Reduce the heat to medium. Add the diced onion, bell peppers, and celery to the pot. Sauté them in the remaining fat, scraping up any brown bits from the bottom of the pot. Cook for 4 to 5 minutes until the onions are translucent and the vegetables have softened. Add the minced garlic and cook for one more minute, until it is fragrant.

Add the dry orzo pasta directly to the pot with the vegetables. Stir constantly for about 2 minutes. The orzo will turn a shade darker and smell nutty and toasty.

Pour in the chicken broth and the remaining Cajun seasoning. Stir well to combine, making sure to scrape up any remaining bits from the bottom. Bring the mixture to a gentle boil. You will see the liquid turn a beautiful, rich amber color.

Once boiling, reduce the heat to low, cover the pot, and let it simmer for 10 to 12 minutes. Do not lift the lid! Let the steam do its work. The orzo will absorb the broth and become tender. The liquid will thicken into a starchy, creamy sauce.

Remove the lid. Stir in the heavy cream (or coconut milk), the cooked chicken (along with any juices on the plate), and the cayenne pepper if you like heat. Stir gently and let it cook for another 2 minutes, until the chicken is heated through and the sauce is creamy. Turn off the heat. Stir in the grated Parmesan cheese. Watch it melt into the sauce, creating a silky, luscious finish. Taste and add salt and pepper as needed. Garnish with fresh parsley.