In a large saucepan, melt butter over medium heat. Whisk in flour and cook 1 minute.
Gradually whisk in broth and milk. Bring to a gentle boil and cook for 2-3 minutes until thick.
Add broccoli florets and simmer 5 minutes until tender.
Turn off heat. Add shredded cheese and garlic powder. Stir until cheese is melted.
Season with salt and pepper.