In a stock pot, melt butter over medium heat. Cook onion in butter until softened. Stir in broccoli and cover with chicken broth. Simmer until broccoli is tender, 10-15 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.