Pat the chicken thighs dry with paper towels. Season both sides with salt and black pepper.
In a large deep skillet or Dutch oven, melt 2 tablespoons of butter over medium-high heat.
Add the chicken thighs skin-side down and cook for 5-7 minutes until the skin is golden brown and crispy. Flip and cook the other side for 3-4 minutes. Remove chicken from the skillet and set aside.
Reduce heat to medium. Add the remaining 1 tablespoon of butter to the skillet.
Add the chopped onion and cook for 3-4 minutes until softened and translucent.
Add the minced garlic and cook for 1 minute until fragrant, stirring frequently to avoid burning.
Add the rinsed rice to the skillet and stir to coat the rice with the butter, onion, and garlic mixture.
Pour in the chicken broth, then add dried thyme, paprika, and crushed red pepper flakes. Stir well to combine.
Return the chicken thighs to the skillet, placing them on top of the rice mixture skin-side up.
Bring the liquid to a gentle boil, then reduce heat to low. Cover the skillet with a tight-fitting lid and simmer for 20 minutes, or until the rice is tender and the chicken is cooked through (internal temperature of 165°F/74°C).
Remove the skillet from heat and let it rest, covered, for 5 minutes.
Sprinkle chopped fresh parsley over the chicken and rice before serving.