01 - Pat the chicken thighs dry with paper towels. Evenly coat both sides with salt, black pepper, and paprika, pressing the seasonings into the skin for maximum adhesion.
02 - Heat olive oil in a large skillet or Dutch oven over medium-high heat. Place 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 thighs to a plate and set aside.
03 - Reduce the heat to medium. Melt butter in the same pan, then add the chopped onion, diced celery, and bell pepper. Sauté for 4 to 5 minutes until the vegetables have softened. Stir in the minced garlic and cook for an additional minute until fragrant.
04 - Sprinkle flour over the softened vegetables and stir continuously for about 1 minute, allowing the flour to cook off its raw taste and form a light roux.
05 - Gradually pour in the chicken broth and milk (or cream), whisking constantly to prevent lumps from forming. Add the dried thyme and cayenne pepper if using. Continue stirring until the mixture is smooth and begins to thicken slightly.
06 - Stir the long-grain white rice into the sauce until evenly distributed. Nestle the browned chicken thighs on top of the rice mixture, skin-side up, so the skin remains exposed for crisping.
07 - Bring the liquid 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 (74°C).
08 - Remove the pan from heat and let it rest covered for 5 minutes to allow the sauce to settle. Garnish with chopped fresh parsley and serve directly from the skillet or Dutch oven.