Preheat the oven to 375°F (190°C).
In a 9×13-inch baking dish, spread the uncooked rice evenly.
Pour the chicken broth over the rice, making sure it is evenly distributed.
Add the chopped onion and frozen peas over the rice mixture.
In a large bowl, combine the cream of mushroom soup, cream of chicken soup, garlic powder, dried thyme, salt, and black pepper. Stir until well mixed.
Add the chicken pieces to the soup mixture and stir to coat evenly.
Pour the chicken and soup mixture evenly over the rice and vegetables in the baking dish. Do not stir.
Cover the baking dish tightly with aluminum foil.
Bake in the preheated oven for 50 minutes.
Remove the foil and sprinkle the shredded cheddar cheese evenly over the casserole.
Return the casserole to the oven, uncovered, and bake for an additional 10 minutes, or until the cheese is melted and bubbly and the chicken is cooked through.
Remove from the oven and let it rest for 5 minutes before serving.