Preheat the oven to 375°F (190°C).
Steam the broccoli florets until just tender, about 4-5 minutes. Drain and set aside.
In a medium saucepan, melt the butter over medium heat.
Whisk in the flour and cook for 1-2 minutes until it forms a smooth paste and is lightly golden.
Slowly whisk in the milk, continuing to whisk until the mixture thickens, about 5-7 minutes.
Remove the sauce from heat and stir in the cheddar cheese, mozzarella cheese, garlic powder, onion powder, salt, and black pepper until the cheese is fully melted and the sauce is smooth.
In a large mixing bowl, combine the cooked chicken, steamed broccoli, and cheese sauce. Stir well to combine.
Transfer the mixture to a greased 9×13 inch baking dish and spread evenly.
In a small bowl, mix the breadcrumbs with olive oil until evenly coated.
Sprinkle the breadcrumb mixture evenly over the casserole.
Bake uncovered for 25-30 minutes, until the topping is golden brown and the casserole is bubbly.
Remove from the oven and let cool for 5 minutes before serving.