Preheat the oven: Preheat your oven to 375°F and grease a 9x13 inch baking dish with butter or nonstick spray.
Whisk the sauce: In a medium bowl, whisk together the chicken broth, cream of chicken soup, soy sauce, rice vinegar, salt and pepper until smooth.
Spread the rice: Pour the uncooked rice into the prepared baking dish and spread it into an even layer across the bottom.
Scatter onion and garlic: Sprinkle the diced onion and minced garlic evenly over the rice so their flavor spreads through the dish as it bakes.
Arrange the chicken: Place the chicken thighs on top of the rice in a single layer, leaving a little space between each piece.
Pour the broth mixture: Pour the broth and soup mixture evenly over the chicken and rice, making sure the rice is fully submerged.
Drizzle with butter: Drizzle the melted butter over the top of the chicken for extra richness and browning.
Cover tightly and bake: Cover the dish tightly with foil, sealing the edges well, and bake for 45 minutes.
Check the chicken and rice: Remove the foil and check that the chicken reads 165°F on a meat thermometer and the rice has absorbed most of the liquid.
Add the cheese: Sprinkle the shredded cheddar cheese evenly over the top of the casserole.
Bake uncovered: Return the dish to the oven uncovered and bake another 10 to 15 minutes, until the cheese is melted, golden and bubbly at the edges.
Rest before serving: Let the casserole rest for 5 minutes before serving so the rice finishes absorbing the sauce.