01 - Pat the chicken thighs dry with paper towels. Season both sides generously with salt, black pepper, and paprika, pressing the spices into the skin.
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 until the skin turns deep golden brown. Flip and cook another 4 to 5 minutes. Transfer the browned thighs to a plate and set aside.
03 - Reduce the heat to medium. Melt the butter in the same pan, scraping up any fond. Add the chopped onion, diced celery, and bell pepper. Sauté for 4 to 5 minutes until the vegetables soften. Stir in the minced garlic and cook for 1 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 pour in the chicken broth and milk, whisking steadily to prevent lumps. Add the dried thyme and cayenne pepper if using. Stir until the liquid is smooth and well combined.
06 - Stir the rice into the gravy mixture, distributing it evenly across the pan. Nestle the browned chicken thighs on top, skin-side up, pressing them gently into the liquid.
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 until the rice is tender and the chicken reaches an internal temperature of 165°F.
08 - Remove the pan from heat and let it rest, covered, for 5 minutes. Sprinkle with chopped fresh parsley and serve directly from the skillet.