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 minutes until tender-crisp. Drain and immediately rinse under cold water to stop cooking. Set aside.
In a medium skillet, heat olive oil over medium heat. Add minced garlic and sauté for 1 minute until fragrant.
Add the softened cream cheese and heavy cream to the skillet. Stir continuously until the cream cheese is fully melted and the mixture is smooth.
Remove the skillet from heat and stir in the shredded cheddar cheese, mozzarella cheese, grated Parmesan cheese, salt, black pepper, and onion powder until well combined.
In a large mixing bowl, combine the shredded cooked chicken, blanched broccoli, and cheese sauce. Mix well to evenly coat all ingredients.
Transfer the mixture into a greased 9×13-inch baking dish and spread evenly.
Bake in the preheated oven for 20-25 minutes until the casserole is bubbly and the top is golden brown.
Remove from oven and let it rest for 5 minutes before serving.