Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish.
Steam the broccoli until just tender (about 3 minutes in the microwave with a splash of water, covered).
In a large bowl, mix together the cream of chicken soup, mayonnaise (or sour cream), milk, garlic powder, salt, and pepper. Stir in the diced chicken, cooked rice, steamed broccoli, and 1 cup of the cheddar cheese until everything is well coated.
Spread the mixture evenly in your prepared baking dish.
In a separate bowl, toss together the crushed crackers, melted butter, and remaining 1/2 cup cheddar cheese. Sprinkle this crunchy topping evenly over the casserole.
Bake for 25–30 minutes, until the topping is golden and the casserole is bubbling around the edges.
Let it cool for a few minutes before serving.