Step 1

Preheat oven to 400 degrees F.

Step 2

Heat oil in a large ovenproof skillet over high heat. Add chicken and cook until well browned, about 4 minutes per side. Transfer to a clean cutting board and let stand for 5 minutes. Cut into 1-inch cubes.

Step 3

Whisk flour and 2/3 cup milk in a small bowl. Add the remaining 3 1/3 cups milk to the pan; bring to a boil over medium-high heat. Gradually whisk in the flour-milk mixture. Return to a boil and cook, stirring often, until thickened, 2 to 3 minutes. Stir in rice and broccoli; return to a boil and cook until the broccoli is tender, about 2 minutes. Stir in the chicken, cheese, salt and pepper. Sprinkle onions on top.

Step 4

Transfer the pan to the oven. Bake until the casserole is browned and bubbling, 10 to 12 minutes. Let cool for 5 minutes before serving.