Season the chicken thighs with salt and black pepper on both sides.
Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken thighs skin-side down and cook for 5-7 minutes until the skin is golden brown and crisp. Flip and cook for another 3 minutes. Remove chicken from the pan and set aside.
Reduce heat to medium. Add diced onion, carrot, and celery to the same pan. Cook, stirring occasionally, for 5 minutes until vegetables are softened.
Add minced garlic and cook for 1 minute until fragrant.
Add rinsed rice to the pan and stir to coat the rice with the oil and vegetables.
Pour in chicken broth and add dried thyme, smoked paprika, and cayenne pepper. Stir to combine.
Return the chicken thighs to the pan, placing them on top of the rice mixture skin-side up.
Bring to a gentle simmer, then cover the pan with a tight-fitting lid and reduce heat to low.
Cook for 25 minutes without lifting the lid, until the rice is tender and the chicken is cooked through (internal temperature of 165°F/74°C).
Remove the lid and scatter frozen peas over the rice. Cover again and let sit off heat for 5 minutes to warm the peas.
Sprinkle chopped fresh parsley over the dish before serving.