Preheat the oven to 375°F (190°C).
In a large mixing bowl, combine the shredded chicken and broccoli florets.
In a saucepan over medium heat, combine coconut milk, olive oil, nutritional yeast, garlic powder, onion powder, black pepper, and salt.
Cook the sauce for about 5-7 minutes, stirring frequently, until thickened.
Pour the sauce over the chicken and broccoli mixture, stirring to coat evenly.
Transfer the mixture to a greased 9x13 inch baking dish.
Sprinkle gluten-free breadcrumbs on top of the mixture.
Bake in the preheated oven for 25-30 minutes, until the top is golden and bubbling.
Let the bake rest for 5-10 minutes before serving.