Broccoli Cheese Soup

Another broccoli recipe...I didn't realize I bought so much of it.  But I do like broccoli so that's okay.  When I was pregnant with Kiana I craved broccoli cheese soup, broccoli with cheese sauce, etc. This is a recipe I saw on Allrecipes.  But I changed the recipe how I made it.

Broccoli Cheese Soup
Ingredients:

1/4 cup butter
1 onion, chopped
1 (16 ounce) pkg frozen chopped broccoli--(I used 8 cups of fresh chopped broccoli, not finely chopped--this depends on how much broccoli you want in the soup)
4 (14.5 oz) cans chicken broth (or 7.5 cups water mixed with chicken bouillon)
1 (1 pound) processed cheese (like Velveeta), cubed
2 cups milk
1 tbsp garlic powder
2/3 cup cornstarch
1 cup water
1/4 tsp black or white pepper

Directions:
In a large 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.