Preheat the oven to 375°F.
In a large mixing bowl, combine the cooked chicken, steamed broccoli, heavy cream, half of the mozzarella cheese, Parmesan cheese, garlic, Italian seasoning, salt, black pepper, and red pepper flakes. Mix until well combined.
Grease a 9x13-inch baking dish with olive oil.
Pour the chicken and broccoli mixture into the dish, spreading it evenly.
Top with the remaining mozzarella cheese.
Bake in the preheated oven for 25-30 minutes, or until the cheese is bubbly and golden brown.
Remove from the oven and let it cool for 5 minutes before serving.