Season the cut chicken pieces evenly with 1 tablespoon of the Cajun seasoning, thyme, and black pepper.
Heat the olive oil in a large skillet over medium-high heat. Add the seasoned chicken and cook until browned on all sides and cooked through, about 5 to 7 minutes. Remove the chicken from the skillet and set aside.
Reduce the heat to medium. Add the chopped onion and bell pepper to the same skillet. Cook until softened, about 5 minutes.
Add the minced garlic and the remaining 1 tablespoon of Cajun seasoning to the vegetables. Cook for 1 minute until fragrant.
Pour in the chicken broth, scraping up any browned bits from the bottom of the skillet. Bring the liquid to a simmer.
Stir in the heavy cream. Let the sauce simmer gently for 2 minutes until it begins to thicken slightly.
Reduce the heat to low. Stir in the Parmesan cheese until the sauce is smooth and creamy. Taste the sauce and add more Cajun seasoning if you desire more heat or flavor.
Return the cooked chicken to the skillet. Stir to coat the chicken in the creamy sauce. Cook for 1 minute to heat through.
Serve the creamy Cajun chicken immediately over the cooked white rice. Garnish with fresh parsley.
Notes
For a spicier sauce, increase the amount of Cajun seasoning to 3 tablespoons or add 1/4 teaspoon of cayenne pepper with the dry spices.
If you prefer a thicker sauce, mix 1 teaspoon of cornstarch with 1 tablespoon of cold water and stir this slurry into the simmering sauce before adding the cheese.
You can substitute smoked sausage for half of the chicken for added flavor.