Preheat the oven to 350 degrees F / 180 degrees C.
Melt butter in a large saute pan over medium heat. Add the onion and saute for a bout 5 minutes until tender and translucent. Transfer to a plate.
In the same pan, cook the chicken breast pieces for 6-7 minutes, stirring occasionally. You are browning the chicken in this step and do not need to worry if the chicken is cooked through at this point.
In a large covered baking dish or Dutch oven, combine the chicken broth, rice, cooked chicken, sauteed onions, salt, pepper and one cup of cheddar. Stir well to combine.
Cover with a lid and cook for 35-40 minutes in the oven.
While the casserole bakes, blanch the broccoli florets by dropping them into salted boiling water for 5 minutes. Transfer cooked broccoli to ice water to stop the cooking then drain the broccoli.
Remove the casserole from the oven and stir to combine.
Top with the broccoli and the remaining cheese. Return the casserole to the oven for another 5 minutes to melt the cheese.
Serve immediately.