Take the broccoli out of the freezer and allow it to begin to thaw. Once it’s soft enough to cut with a knife, cut the florets into smaller, bite-sized pieces.
Cut the chicken breast into small 1/2-inch cubes. Season with salt and pepper. Heat a large skillet over medium, then add the olive oil and swirl to coat the surface. Add the chicken pieces and cook until slightly browned on the outside. Remove the chicken pieces to a large clean bowl.
While the chicken is cooking, finely dice the onion, and peel and slice the carrots. Add the onion and carrots to the skillet after the chicken is removed and sauté until the onions are softened. Transfer the onions and carrots to the bowl with the chicken.
Add the chopped broccoli florets (even if not fully thawed) and the cooked rice to the bowl with the chicken, onions, and carrots. Stir to combine, then add 1/2 of the shredded cheddar (about 1 cup) and stir to combine again. Set the mixture aside.
Begin to preheat the oven to 350ºF and coat the inside of a 2 quart casserole dish with non-stick spray. Add the butter and flour to the same skillet used to cook the chicken and vegetables. Cook and whisk the butter and flour over medium heat until it begins to foam, then continue to stir and cook for one minute.
Slowly whisk the chicken broth into the flour and butter mixture. Allow it to come up to a simmer, at which time it will thicken. Once thickened, whisk in the milk and allow it to come up to a simmer again. When it’s thick enough to coat a spoon, season with smoked paprika, freshly cracked pepper, and salt.
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.