Preheat the oven to 375°F (190°C).
Steam the broccoli florets until tender but still crisp, about 5 minutes. Drain and set aside.
In a medium saucepan, melt the butter over medium heat. Add the minced garlic and cook for 1 minute until fragrant.
Add the cream cheese and heavy cream to the saucepan. Stir continuously until the cream cheese is fully melted and the mixture is smooth.
Remove the saucepan from heat and stir in the shredded cheddar cheese, mozzarella cheese, Parmesan cheese, onion powder, salt, black pepper, and crushed red pepper flakes until the cheese is melted and the sauce is creamy.
In a large mixing bowl, combine the shredded cooked chicken, steamed broccoli, and cheese sauce. Mix well to evenly coat the chicken and broccoli.
Transfer the mixture to a greased 9×13-inch casserole dish and spread it out evenly.
Bake in the preheated oven for 20 to 25 minutes, until the casserole is bubbly and the top is lightly golden.
Remove from the oven and let it cool for 5 minutes before serving.