Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
In a large bowl, mix the uncooked rice, cream of mushroom soup, cream of chicken soup, chicken broth, garlic powder, thyme, salt, and black pepper until well combined.
Spread the rice mixture evenly in the prepared baking dish. Add the chopped onion and frozen mixed vegetables, stirring lightly to distribute them throughout the rice.
Nestle the chicken pieces into the rice mixture, pressing them down slightly so they’re partially submerged. Sprinkle the shredded cheddar cheese evenly over the top.
Cover the dish tightly with aluminum foil and bake in the preheated oven for 35-40 minutes, until the rice is tender and the chicken is cooked through (internal temperature of 165°F/74°C). Remove the foil, and if using breadcrumbs or crushed crackers, sprinkle them over the top. Bake uncovered for an additional 5-10 minutes until the cheese is bubbly and the topping is golden.
Let the casserole rest for 5 minutes before serving. Scoop into bowls or plates and enjoy your comforting chicken and rice casserole!