Preheat the oven to 375°F (190°C).
In a large skillet, heat olive oil over medium heat. Add diced onion and minced garlic and sauté for 3-4 minutes until softened.
Add the chicken pieces to the skillet and cook for 5-6 minutes until lightly browned but not fully cooked through.
In a large mixing bowl, combine the cream of mushroom soup, sour cream, milk, dried thyme, salt, and black pepper. Mix well.
Add the uncooked rice, chicken broth, frozen peas, sliced mushrooms, and the sautéed chicken, onion, and garlic mixture to the bowl. Stir everything together until well combined.
Transfer the 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 and sprinkle shredded cheddar cheese evenly over the top.
Return the casserole to the oven, uncovered, and bake 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.