Preheat the oven to 375°F (190°C).
Heat olive oil in a large oven-safe skillet or Dutch oven over medium-high heat.
Season the chicken thighs with salt and black pepper on both sides.
Place the chicken thighs skin-side down in the skillet and sear for 5-6 minutes until the skin is golden brown and crispy. Flip and cook for another 3 minutes. Remove chicken from skillet and set aside.
Reduce heat to medium. Add chopped onion, carrot, and celery to the skillet. Sauté for 5 minutes until vegetables are softened.
Add minced garlic and cook for 1 minute until fragrant.
Stir in the rinsed rice, coating it well with the vegetable mixture.
Pour in the chicken broth and heavy cream. Add dried thyme and paprika. Stir to combine and bring to a gentle simmer.
Nestle the chicken thighs back into the skillet on top of the rice mixture, skin-side up.
Transfer the skillet to the preheated oven and bake uncovered for 35 minutes, or until the rice is tender and the chicken is cooked through (internal temperature 165°F/74°C).
Remove the skillet from the oven. Sprinkle frozen peas evenly over the rice and chicken, then sprinkle shredded cheddar cheese on top.
Return the skillet to the oven and bake for an additional 5 minutes, or until the cheese is melted and peas are heated through.
Remove from oven and let rest for 5 minutes before serving.
Garnish with chopped fresh parsley and serve warm.