Preheat the oven to 375°F with a rack centered in the oven. Lightly coat an 11x7-inch or 1.5-quart baking dish with cooking spray and set it aside.
Place a large skillet over medium heat and melt the butter. Once melted, stir in the diced yellow onion along with 1 1/2 teaspoons of kosher salt. Cook the onions until they turn soft and translucent, about 3 to 5 minutes, ensuring they don’t brown.
Sprinkle the flour into the skillet, stirring continuously to evenly coat the mixture. Let it cook for 1 minute to eliminate the raw taste of the flour.
Gradually whisk in the chicken broth, ensuring any lumps are smoothed out and the bottom of the pan is scraped clean. Pour in the milk along with 1/4 teaspoon of the black pepper. Continue stirring and bring the mixture to a gentle boil. Allow it to simmer for around 3 minutes or until the sauce thickens.
Into the prepared baking dish, place the uncooked rice and frozen mixed vegetables. Pour the creamy sauce over and mix gently to distribute the ingredients evenly.
Rub the remaining 1/2 teaspoon salt and 1/2 teaspoon black pepper onto the chicken thighs. Lay the seasoned chicken pieces over the rice and vegetable mixture. Cover the dish tightly with aluminum foil.
Bake the covered casserole for 1 hour, or until the rice is fully cooked and a thermometer inserted into the thickest part of the chicken reads 160°F.
Turn off the oven. Remove the foil and scatter the shredded cheddar cheese over the top. Place the dish back into the warm oven, uncovered, for 2 to 4 minutes or until the cheese melts completely.