Preheat your oven to 375°F (190°C) and grease a 9x13-inch baking dish with cooking spray or butter.
In a large bowl, combine cooked chicken with steamed broccoli florets and optional cauliflower rice.
In a medium saucepan over medium heat, whisk together heavy cream, sour cream, and softened cream cheese until smooth. Stir in garlic powder, onion powder, smoked paprika, salt, and black pepper. Mix in 1 cup of shredded cheddar cheese until melted.
Pour the cheese sauce over the chicken and vegetable mixture, toss gently to coat, and transfer to the prepared baking dish.
Sprinkle the remaining shredded mozzarella and cheddar cheese on top, and optionally add grated Parmesan cheese.
Bake for about 25-30 minutes until bubbling and golden brown on top.
Let it rest for about 5 minutes before serving warm.