Gather and prepare all ingredients. Preheat the oven to 350°F and spray an 8x10 casserole dish with nonstick spray and set aside.
Cook the rice according to the package. This should yield 4 cups of cooked rice.
While the rice cooks, cut the chicken into ½-inch cubes and season with ½ tsp salt and ½ tsp pepper. Heat a large skillet over medium-high heat, add the olive oil, and sear the chicken for about 2 minutes per side until lightly browned. Transfer to a large bowl.
Turn the heat to medium and add the onion and carrots to the skillet and sauté until the onions are softened, for about 5 minutes. Transfer the onions and carrots to the bowl with the chicken.
In the same skillet, add the butter and flour. Cook over medium heat, whisking constantly, until the mixture becomes foamy, then continue cooking for about one more minute.
Slowly whisk in the chicken broth and bring the mixture to a simmer until thickened. Whisk in the milk and simmer again until the sauce coats a spoon. Turn off the heat and season with the smoked paprika, garlic powder, onion powder, and the remaining salt and pepper.
Add the chopped broccoli florets, cooked rice, and ½ of the shredded cheddar (about 1 cup) to the bowl with the chicken, onions, and carrots.
Pour the sauce over the rice mixture in the bowl and stir until everything is combined and coated in sauce. Transfer the mixture to the casserole dish. Sprinkle the remaining shredded cheese over the casserole.
Bake the casserole, uncovered, for about 35 minutes or until it becomes golden brown around the edges. Serve hot.
*I use boneless, skinless chicken breast in this casserole to keep it classic, but you can use diced chicken thighs if that's a better fit for your budget.
**I use Better Than Bouillon to make my broth. If you use a low sodium broth, you may need to add extra salt to the sauce to get the best flavor.
***Frozen or fresh broccoli will work. Steam or boil fresh broccoli until al dente before using.