Step 1

Heat the oven and prepare the baking dish. Arrange a rack in the middle of the oven and heat the oven to 375°F. Coat an 11x7-inch or 1 1/2-quart baking dish with cooking spray; set aside.

Step 2

Sauté the onion in butter. Melt 3 tablespoons unsalted butter in a large skillet over medium heat. Add 1 cup diced yellow onion and 1 1/2 teaspoons of the kosher salt and sauté until onion is soft but not browned, 3 to 5 minutes.

Step 3

Stir in the flour. Sprinkle in 3 tablespoons all-purpose flour and cook for 1 minute, stirring constantly to coat the flour in the butter and to cook off the raw flour flavor.

Step 4

Add the chicken broth and milk and cook until thickened. Pour in 1 3/4 cups low-sodium chicken broth and whisk to incorporate, breaking up any lumps of flour and onion and scraping browned bits from the bottom of the pan. Pour in 1/2 cup whole or 2% milk and 1/4 teaspoon of the black pepper and whisk to completely incorporate. Bring to a boil, stirring constantly, until sauce thickens, about 3 minutes.

Step 5

Add sauce to rice and vegetables in baking dish. Place 3/4 cup uncooked long-grain white rice and 3 cups frozen mixed vegetables in the prepared baking dish. Pour in the sauce and stir to combine.

Step 6

Season the chicken and lay on the rice mixture. Season 1 1/2 pounds boneless, skinless chicken thighs all over with the remaining 1/2 teaspoon kosher salt and remaining 1/2 teaspoon black pepper. Nestle the chicken on top of the rice mixture. Cover the baking dish tightly with aluminum foil.

Step 7

Bake for 1 hour. Bake until the rice is tender and an instant-read thermometer inserted into the thickest part of the chicken registers 160°F, about 1 hour.

Step 8

Top with shredded cheese. Turn the oven off. Uncover and sprinkle with 1/2 cup shredded cheddar cheese. Return to the still-warm oven uncovered and let sit until the cheese melts, 2 to 4 minutes.