Preheat the oven to 375°F / 190°C.
Lightly grease a 9-by-13-inch baking dish with butter, oil, or nonstick cooking spray.
Cook the broccoli for 2–3 minutes, until bright green and slightly tender.
Drain the broccoli thoroughly and set it aside.
Heat the butter or olive oil in a skillet over medium heat.
Add the diced onion and cook for 3–4 minutes, until softened.
Add the minced garlic and cook for another 30 seconds.
In a large bowl, combine the condensed cream of chicken soup, milk, sour cream, garlic powder, onion powder, paprika, salt, and black pepper.
Stir in the cooked onion and garlic.
Add the cooked chicken and rice to the creamy mixture.
Stir gently until the chicken and rice are evenly coated.
Fold in the broccoli and 1½ cups of shredded cheddar cheese.
Transfer the mixture to the prepared baking dish and spread it evenly.
Sprinkle the remaining ½ cup of cheddar cheese over the top.
For the optional crunchy topping, combine the crushed crackers or breadcrumbs with melted butter and Parmesan cheese.
Sprinkle the crunchy mixture evenly over the casserole.
Cover the baking dish loosely with foil.
Bake for 20 minutes.
Remove the foil and bake for another 10–15 minutes, until the casserole is hot, bubbling, and lightly golden.
Let the casserole rest for 5–10 minutes before serving.
Garnish with chopped green onions, parsley, or additional black pepper, if desired.