Place a stockpot over medium heat.
Add butter and heat until melted and hot.
Place onion in pot and cook until softened.
Stir in broccoli.
Cover with chicken broth. Allow to simmer until broccoli is tender, about 10 to 15 minutes. Reduce heat.
Add cheese cubes. Cook, stirring constantly, until melted.
Add milk and garlic powder. Mix well.
In a small bowl, stir cornstarch into water until dissolved. Stir into soup.
Continue to cook, stirring frequently, until soup thickens.