Preheat the oven to 375°F (190°C).
Season the chicken thighs with salt and black pepper on both sides.
In a large oven-safe pot or Dutch oven, heat the olive oil over medium-high heat.
Add the chicken thighs skin-side down and sear for 5-6 minutes until the skin is golden brown and crispy. Flip and cook for another 3 minutes. Remove the chicken from the pot and set aside.
Reduce the heat to medium. Add the diced onion, carrot, and celery to the pot and sauté for 5 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Add the rinsed rice to the pot and stir to coat it with the vegetables and oil.
Pour in the chicken broth, then stir in the dried thyme and paprika.
Return the chicken thighs to the pot, placing them on top of the rice mixture, skin-side up.
Bring the mixture to a simmer, then cover the pot with a lid and transfer it to the preheated oven.
Bake for 35 minutes covered.
Remove the pot from the oven, uncover, and sprinkle the frozen peas evenly over the rice.
Sprinkle the shredded cheddar cheese on top of the peas and chicken.
Return the pot to the oven uncovered and bake for an additional 5-7 minutes until the cheese is melted and bubbly.
Remove from the oven and let the casserole rest for 5 minutes.
Garnish with chopped fresh parsley before serving.