Preheat the oven to 350°F (175°C). Lightly grease a 9×13 inch casserole dish.
In a medium saucepan, bring the chicken broth to a boil. Stir in the uncooked rice, reduce heat to low, cover, and simmer for 15 minutes until rice is tender and liquid is absorbed.
While the rice cooks, steam the broccoli florets until tender-crisp, about 4-5 minutes. Drain and set aside.
In a large skillet, melt the butter over medium heat. Add the chopped onion and cook until translucent, about 3-4 minutes.
Add the minced garlic to the skillet and cook for 1 minute until fragrant.
Sprinkle the flour over the onions and garlic, stirring constantly for 2 minutes to form a roux.
Gradually whisk in the milk and continue whisking until the sauce thickens, about 3-4 minutes.
Remove the skillet from heat and stir in the salt, black pepper, and paprika.
In a large mixing bowl, combine the cooked chicken, steamed broccoli, cooked rice, and cheese (reserve 1/4 cup cheddar cheese for topping).
Pour the prepared sauce over the mixture and gently fold everything together until evenly coated.
Transfer the mixture to the prepared casserole dish and spread evenly.
Sprinkle the reserved cheddar cheese evenly over the top.
Bake in the preheated oven for 20-25 minutes, until the casserole is bubbly and the cheese is melted and lightly golden.
Remove from oven and let rest for 5 minutes before serving.