In a stockpot, melt butter over medium heat. Cook onion in butter until softened. Stir in broccoli, and cover with chicken broth. Simmer until broccoli is tender, 10 to 15 minutes.
Reduce heat, and stir in cheese cubes until melted. Mix in milk and garlic powder.
In a small bowl, stir cornstarch into water until dissolved. Stir into soup; cook, stirring frequently, until thick.