Season the chicken with Cajun seasoning, smoked paprika, garlic powder, black pepper, and salt. Heat the olive oil and 1 tablespoon butter in a large deep skillet or Dutch oven over medium-high heat. Cook the chicken until golden-brown with lightly seared edges and fully cooked, then transfer it to a plate.
Lower the heat to medium and melt another tablespoon of butter in the same pot. Add the onion and red bell pepper and cook for 3 to 4 minutes until softened. Stir in the garlic and cook for about 30 seconds.
Add the drained tomatoes and rice, stirring for about 1 minute so the grains pick up the Cajun seasoning and buttery pan flavors.
Pour in the chicken broth and bring everything to a gentle simmer. Cover, reduce the heat to low, and cook for 18 to 20 minutes, until the rice is tender and most of the liquid has been absorbed.
Remove from the heat and let the rice rest, covered, for 5 minutes. Stir in the remaining butter and heavy cream, then return the chicken and mix everything together thoroughly so the chicken is evenly distributed throughout the rice. Finish with green onions and parsley.