Preheat the oven: Preheat the oven to 375°F and lightly grease a 9x13-inch baking dish.
Whisk the base: In the baking dish, whisk together the chicken broth, cream of chicken soup, onion powder, garlic powder, and the soy sauce and rice vinegar mixture until smooth.
Stir in rice and vegetables: Add the raw rice and frozen peas and carrots to the dish, stirring until everything is evenly coated in the liquid.
Add the chicken: Nestle the chicken thighs on top of the rice mixture, pressing them down slightly so they sit partly submerged. Season the tops with salt and pepper.
Cover tightly: Cover the dish tightly with aluminum foil to trap steam, which is what cooks the raw rice through.
Bake covered: Bake covered for 45 minutes, until the rice is tender and the chicken reaches an internal temperature of 165°F.
Add cheese: Remove the foil and scatter the shredded cheddar evenly over the top of the casserole.
Finish uncovered: Return the dish to the oven uncovered and bake 10 more minutes, until the cheese turns golden and bubbly at the edges.
Rest before serving: Let the casserole rest for 5 minutes so the rice firms up slightly, making it easier to scoop and serve.