Steam broccoli until crisp tender; about 10 minutes. Chop into bite sized pieces and set aside.
In a large pot over medium heat, melt the butter. Add onion to butter and cook until onions becoming translucent; about 5 minutes. Add garlic and minced chipotle peppers; cook and stir for one minute. Add salt and pepper.
Sprinkle the flour over the mixture and stir until everything is combined. Slowly add the milk and half & half; stir until mixture is smooth. Let the sauce simmer, reducing the heat if necessary, about 5 minutes, until thickened and bubbling.
Slowly add the cheddar cheese, stirring until cheese is completely incorporated and mixture is smooth.
Add broccoli, rice, and chicken to the pot and mix well.
Transfer mixture to a casserole dish and bake 30-35 minutes, until the top is nicely browned.