Preheat the oven to 375°F (190°C).
Bring a large pot of salted water to a boil. Add the broccoli florets and cook for 3 minutes until bright green and slightly tender. Drain 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, and mayonnaise to the skillet. Stir continuously until the cream cheese is melted and the mixture is smooth.
Remove the skillet from heat and stir in the shredded cheddar cheese, mozzarella cheese, Parmesan cheese, onion powder, salt, and black pepper until well combined.
In a large mixing bowl, combine the shredded cooked chicken, blanched broccoli, and cheese sauce. Mix until everything is evenly coated.
Transfer the mixture to a greased 9×13-inch casserole dish and spread it evenly.
Bake in the preheated oven for 30 minutes, or until the casserole is bubbly and the top is golden brown.
Remove from the oven and let it cool for 5 minutes before serving.