01 - Pat the chicken thighs dry with paper towels. Season both sides generously with salt, black pepper, and paprika, ensuring even coverage.
02 - Heat olive oil in a large skillet or Dutch oven over medium-high heat. Place the chicken thighs skin-side down and sear for 4 to 5 minutes per side until the skin turns a deep golden brown. Transfer the browned chicken to a plate and set aside.
03 - Reduce the heat to medium. In the same pan, melt the butter. Add the chopped onion, diced celery, and bell pepper, sautéing for 4 to 5 minutes until the vegetables soften. Stir in the minced garlic and cook for 1 additional minute until fragrant.
04 - Sprinkle the flour over the sautéed vegetables and stir continuously for 1 minute to cook off the raw flour taste and form a light roux.
05 - Gradually whisk in the chicken broth followed by the milk or cream, stirring constantly to prevent lumps from forming. Add the dried thyme and cayenne pepper if using. Continue stirring until the mixture comes together into a smooth, creamy sauce.
06 - Stir the raw rice into the sauce until evenly distributed. Nestle the browned chicken thighs on top of the rice, positioning them skin-side up. Press them gently into the liquid without submerging the skin.
07 - Bring the mixture to a gentle simmer. Reduce the heat to low, cover with a tight-fitting lid, and cook for 25 to 30 minutes. The rice should be tender and the chicken should reach an internal temperature of 165°F. Avoid lifting the lid during cooking.
08 - Remove the pan from heat and let it rest, covered, for 5 minutes to allow the sauce to thicken slightly. Garnish with chopped fresh parsley and serve directly from the skillet.