Cream of Broccoli Soup with Cheese

At long last, I tracked down a copy of my mom's easy, cheesy and delicious Cream of Broccoli soup recipe! I'm sure modifications could be made to use fresh broccoli rather than frozen, and if you're some kind of cheese snob, feel free to grate your own. I haven't tried using fresh broccoli, but when I do you'll be the first to hear about it. Sorry I don't remember how many servings this makes, but it will feed a family.

For now, this soup is simple and comforting, just perfect for crisp fall days.

Cream of Broccoli Soup with Cheese

1 medium onion, diced
1 large can chicken broth (I think mom means the really big ones, around 46 ounces?)
2 boxes frozen chopped broccoli
2 cups shredded cheddar cheese
3 cups half and half

Cream Sauce: 1/2 cup butter, 1/2 cup flour

Cook onion and broccoli in broth until tender, about 20 minutes. Make Cream Sauce in separate pan--melt butter, blend in flour until smooth. Add Cream Sauce to broth and cook about 5 minutes to blend, stirring constantly. Remove from heat, stir in cheese until blended and melted. Add half and half. Return to low heat and keep hot until serving.

Note: I haven't made this in a long time, although my mom made it at my brother's house a while back. I would probably saute the onions in some butter first until translucent, and if I was using fresh broccoli I would saute it with the onions. I'll report back next time I make this.