Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken, steamed broccoli, cheddar cheese, cream of chicken soup, milk, garlic powder, onion powder, black pepper, and salt. Mix until well combined.
Transfer the chicken and broccoli mixture into a greased 9x13 inch baking dish, spreading it evenly.
In a separate bowl, mix the breadcrumbs with olive oil until they are well coated. Sprinkle the breadcrumb mixture evenly over the top of the chicken and broccoli mixture.
Bake in the preheated oven for 25-30 minutes, or until the top is golden brown and the mixture is bubbly.
Remove from the oven and let it cool for a few minutes before serving.