Z.S.
Cheddar cheese in broccoli soup is wonderful. Go for it!
Here is a link to Allrecipes.com and brocc/cheddar soup. http://allrecipes.com/Recipe/Best-Broccoli-Cheddar-Soup/D...
No oily slick, I use cheddar all the time for cream of brocc or cream of cauliflower soup.
You can use chicken broth in the soup. DON'T boil it or it will break down.