Preheat the oven to 375°F (190°C).
Bring a large pot of water to a boil. Add the broccoli florets and cook for 2-3 minutes until bright green and slightly tender. Drain and immediately transfer to a bowl of ice water to stop the cooking process. Drain again and set aside.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for 1 minute until fragrant.
Add the softened cream cheese, heavy cream, mayonnaise, onion powder, salt, and black pepper to the skillet. Stir continuously until the cream cheese melts and the sauce is smooth and creamy.
Remove the skillet from heat and stir in the shredded cheddar cheese and half of the mozzarella cheese until melted and combined.
In a large mixing bowl, combine the shredded cooked chicken, blanched broccoli, and cheese sauce. Mix well to evenly coat the chicken and broccoli.
Transfer the mixture to a greased 9×13 inch baking dish. Sprinkle the remaining mozzarella cheese and grated Parmesan cheese evenly over the top.
Bake in the preheated oven for 25-30 minutes, or until the casserole is bubbly and the cheese on top is golden brown.
Remove from the oven and let cool for 5 minutes before serving.