Preheat your oven to 375°F (190°C).
In a small bowl, combine salt, black pepper, and paprika.
Pat the chicken thighs dry with paper towels. Rub the seasoning mixture evenly over both sides of the chicken thighs.
Heat olive oil in a large oven-safe skillet or casserole dish over medium-high heat. Add the chicken thighs skin-side down and sear for 4-5 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, reduce heat to medium. Add the chopped onion and diced carrot. Sauté for 4-5 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the rinsed rice, coating it well with the oil and vegetables.
Pour in the chicken broth and water, and stir to combine. Bring the mixture to a gentle simmer.
Nestle the seared chicken thighs skin-side up into the rice mixture.
Cover the skillet or casserole dish with a tight-fitting lid or aluminum foil.
Bake in the preheated oven for 40 minutes.
Remove the cover and sprinkle the frozen peas evenly over the rice. Bake uncovered for an additional 10 minutes, or until the rice is tender and the chicken reaches an internal temperature of 165°F (74°C).
Sprinkle shredded cheddar cheese evenly over the casserole. Return to the oven for 5 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.