Heat olive oil in a large oven-safe skillet over medium-high heat.
Add the chicken pieces to the skillet and cook for 5-6 minutes, stirring occasionally, until browned on all sides but not fully cooked through. Remove chicken from skillet and set aside.
In the same skillet, add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Stir in the rinsed rice, coating it well with the oil and cooking for 1-2 minutes.
Pour in the chicken broth and add the frozen peas and carrots, diced red bell pepper, dried thyme, smoked paprika, salt, and black pepper. Stir to combine.
Return the browned chicken pieces to the skillet, nestling them into the rice mixture.
Bring the mixture to a gentle boil, then reduce heat to low and cover the skillet with a tight-fitting lid.
Simmer for 25 minutes without lifting the lid, until the rice is tender and the chicken is cooked through.
Remove the skillet from heat and sprinkle shredded cheddar cheese evenly over the top.
Cover the skillet again and let it sit for 5 minutes to allow the cheese to melt.
Sprinkle chopped fresh parsley over the casserole before serving.