Heat the olive oil in a large oven-safe skillet over medium heat.
Add the chicken pieces and cook for 5-6 minutes, stirring occasionally, until lightly browned but not fully cooked. Remove chicken from skillet and set aside.
In the same skillet, add the diced onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Stir in the uncooked rice, coating it well with the oil and onion mixture.
Pour in the chicken broth and whole milk, then add the frozen peas and carrots.
Season with dried thyme, dried basil, paprika, salt, and black pepper. Stir to combine.
Return the 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 lid.
Simmer for 25-30 minutes, or until the rice is tender and the chicken is cooked through.
Remove the lid and sprinkle the shredded cheddar cheese evenly over the top.
Cover again and cook for an additional 3-5 minutes until the cheese is melted.
Remove from heat and let the casserole sit covered for 5 minutes before serving.