Preheat the oven to 375°F (190°C).
In a large skillet, heat olive oil over medium heat. Add chopped onion and cook for 3-4 minutes until softened.
Add minced garlic to the skillet and cook for an additional 1 minute until fragrant.
Add the chicken pieces to the skillet and cook until they are no longer pink on the outside, about 5-6 minutes. Remove from heat.
In a large mixing bowl, combine the uncooked rice, chicken broth, cream of mushroom soup, sour cream, milk, dried thyme, salt, black pepper, and paprika. Stir until well combined.
Fold in the cooked chicken, sautéed onions and garlic, and frozen peas into the rice mixture.
Pour the entire mixture into a greased 9×13 inch baking dish and spread evenly.
Cover the baking dish tightly with aluminum foil and bake in the preheated oven for 40 minutes.
Remove the foil, sprinkle shredded cheddar cheese evenly over the top, and bake uncovered for an additional 5 minutes or until the cheese is melted and bubbly.
Remove from the oven and let the casserole rest for 5 minutes before serving.