Melt butter in a saucepan over medium heat. Cook the onion until soft. Add broccoli and season with chicken stock. Simmer until broccoli is tender, 10 to 15 minutes.
Reduce heat and add cubes of cheese to cook until melted. Mix milk with garlic powder and add to the soup.
In a small bowl, mix corn starch in water until completely dissolved. Add to the soup with plenty of stirring.