Preheat the oven to 350°F (175°C).
In a medium saucepan, bring chicken broth to a boil. Add the rice, reduce heat to low, cover, and simmer for 15 minutes or until rice is tender and liquid is absorbed.
Meanwhile, heat olive oil in a large skillet over medium heat. Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic and chicken pieces to the skillet. Cook for 6-8 minutes, stirring occasionally, until chicken is cooked through and no longer pink.
Stir in frozen mixed vegetables and cook for 2 more minutes until vegetables are thawed.
In a large mixing bowl, combine the cooked rice, chicken and vegetable mixture, cream of mushroom soup, sour cream, dried thyme, salt, and black pepper. Mix well to combine.
Transfer the mixture to a greased 9×13-inch baking dish. Spread evenly.
Sprinkle shredded cheddar cheese evenly over the top of the casserole.
Bake uncovered in the preheated oven for 25-30 minutes, until the casserole is bubbly and the cheese is melted and golden brown.
Remove from oven and let rest for 5 minutes before serving.