Season the chicken. Pat the chicken dry. Toss with 1 tablespoon Cajun seasoning, 1/2 teaspoon salt (if needed), and a few grinds of pepper. Let it sit while you prep the vegetables.
Brown the chicken. Heat the olive oil and 1 tablespoon butter in a large heavy pot or Dutch oven over medium-high heat.
Add chicken in a single layer and cook until lightly browned, about 3–4 minutes per side. It doesn’t need to be fully cooked. Remove to a plate.
Sauté the aromatics. Lower heat to medium.
Add remaining 1 tablespoon butter. Sauté onion and bell peppers with a pinch of salt until soft and glossy, 4–5 minutes. Stir in garlic and cook 30 seconds until fragrant.
Toast the spices and rice. Stir in remaining Cajun seasoning, paprika, and the rinsed rice.
Cook 1 minute, stirring, to coat the grains and wake up the spices.
Deglaze and simmer. Pour in the chicken broth, scraping up any browned bits. Return chicken (and any juices) to the pot. Bring to a gentle boil, then reduce to low, cover, and simmer 15–18 minutes, until most liquid is absorbed and rice is tender.
Avoid lifting the lid too often.
Make it creamy. Stir in heavy cream and cream cheese (if using). If adding andouille or veggies like peas/corn, fold them in now. Simmer, uncovered, 2–3 minutes, stirring occasionally, until creamy and slightly thickened.
Finish and balance. Turn off heat.
Stir in Parmesan (if using) and lemon juice. Taste and adjust seasoning with salt, pepper, or a pinch of cayenne for heat.
Garnish and serve. Sprinkle with parsley or green onions. Serve hot, with extra lemon wedges on the side.