Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine shredded chicken and broccoli florets.
Add cream of chicken soup and sour cream to the bowl.
Mix in half of the cheddar cheese, garlic powder, salt, and pepper.
Grease a baking dish with olive oil.
Pour the chicken and broccoli mixture into the prepared dish.
Top with the remaining cheddar cheese.
Evenly spread breadcrumbs over the top.
Bake in the preheated oven for 25-30 minutes until bubbly and golden.
Allow to cool slightly before serving.