Melt butter in a large pot over medium-high heat. Add onion and cook for 3-5 minutes or until tender. Add minced garlic and sauté for an additional minute. Whisk in flour and cook for a few minutes until golden brown.
Reduce heat to low then add chicken stock and milk and stir to combine. Season with salt, pepper, garlic powder and onion powder. Let cook for 5 minutes or until slightly thickened.
Add broccoli and chicken and let simmer for 20 minutes, or until broccoli is tender.
Mix in cheddar cheese and parmesan cheese until melted and combined then remove from heat and serve.