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 5-6 minutes until the skin is golden brown and crispy. Flip and cook for another 3 minutes. Remove chicken from the skillet and set aside.
In the same skillet, add the diced onion and carrot. Sauté for 4-5 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Add the rinsed rice to the skillet and stir to coat the rice with the oil and vegetables.
Pour in the chicken broth, then add smoked paprika and dried thyme. Stir to combine.
Return the chicken thighs to the skillet, placing them on top of the rice mixture, skin-side up.
Bring the mixture to a boil, then reduce heat to low. Cover and simmer for 25 minutes.
After 25 minutes, remove the lid and sprinkle the frozen peas over the rice. Cover and cook for an additional 5 minutes until the rice is tender and the chicken is cooked through (internal temperature of 165°F / 74°C).
Remove from heat and let rest covered for 5 minutes.
Sprinkle chopped fresh parsley over the dish before serving.