Preheat the oven to 350°F (175°C).
Heat olive oil in a large oven-safe skillet or casserole dish over medium heat.
Add the diced onion and minced garlic to the skillet and sauté for 3-4 minutes until softened.
Add the chicken pieces to the skillet and cook for 5-6 minutes until lightly browned on all sides but not fully cooked through.
Stir in the rinsed rice, frozen mixed vegetables, dried thyme, salt, and black pepper.
In a separate bowl, combine the chicken broth, cream of mushroom soup, and sour cream until smooth.
Pour the soup mixture over the chicken and rice mixture in the skillet and stir to combine evenly.
Bring the mixture to a gentle simmer on the stovetop, then cover the skillet with a lid or aluminum foil.
Transfer the covered skillet to the preheated oven and bake for 35 minutes.
Remove the skillet from the oven, uncover, and sprinkle the shredded cheddar cheese evenly over the top.
Return the skillet to the oven and bake uncovered for an additional 5-10 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.