Preheat the oven to 375°F (190°C) and lightly grease a 9x13-inch baking dish.
Bring a pot of water to a boil and blanch the broccoli florets for 2 minutes. Drain and immediately transfer them to a bowl of ice water. Drain well and set aside.
Melt the butter in a large skillet over medium heat. Add the onion and cook for 4 to 5 minutes until softened.
Stir in the garlic and cook for 30 seconds until fragrant.
Sprinkle the flour over the onion mixture and cook for 1 minute, stirring constantly.
Gradually whisk in the chicken broth and milk until smooth. Add the garlic powder, onion powder, salt, and black pepper, then simmer for 3 to 5 minutes until slightly thickened.
Remove the skillet from the heat and stir in 1½ cups of the cheddar cheese and the Parmesan until melted and smooth.
Fold in the cooked chicken, broccoli, and cooked rice until evenly coated in the sauce.
Transfer the mixture to the prepared baking dish and top with the remaining cheddar cheese.
Bake for 20 to 25 minutes, or until the casserole is hot and bubbly. Let it rest for 10 minutes, garnish with fresh parsley, and serve.