Steam the broccoli in a steamer or in a colander over boiling water until tender and bright green, 15 minutes. Set aside.
In a large microwave safe bowl, combine half-and-half, 2 cups water and cheese. Cook in microwave until cheese is melted and smooth, stirring every 2 minutes. Stir in salt, pepper and garlic powder and cook 2 minutes more. In a separate bowl, combine cornstarch and remaining 2 cups water, stirring to dissolve.
Whisk the cornstarch mixture into the soup. Return the soup to the microwave, heating and stirring every 2 minutes until thick. Stir in broccoli; heat once more and serve.
