Broccoli Cheese Soup

I have been looking for a good broccoli soup recipe, because I love Quizno's. I made some adjustments to some recipes I found and this is SO good...just as good as Quizno's and it's super easy.

1/2 cup butter
1 onion, chopped
2 14 oz bags of frozen broccoli
4 14.5 oz cans of chicken broth
2 lbs of Velveeta, cubed
2 cups milk
1 tablespoon garlic powder
2/3 cup corn starch

In a stock pot, melt butter on medium heat. Cook onion in butter until softened. Stir in broccoli and cover with three cans of chicken broth. Simmer until broccoli is tender, 10 - 15 minutes. Reduce heat, stir in cheese until melted. Mix in milk and garlic powder.
In a small bowl, mix final can of broth with corn starch until dissolved. Stir into soup, cook stirring frequently until thick. (I turned the heat up to boil the soup and thickened up very nicely.)
Let cook for about 5 minutes on stove top and serve with warm bread or in a bread bowl.