Set aside a couple cups of chopped broccoli (I just use the florets)
7 cups chicken broth
roughly chopped broccoli (I think this is supposed to be four cups, but I just throw in LOTS)
small onion (sometimes I use one, sometimes I don't)
oregano (like, maybe a couple teaspoons?)
While this is boiling and softening the broccoli, make the sauce:
3 tablespoons butter
6 tablespoons white flour
1 cup milk
2 cups grated cheese
If you don't know how to make a cheese sauce, look it up on the internet. The basic idea is to add everything in little bits and stir a lot until it's smooth and creamy. But if it's not, don't freak out.
Dump the cheese sauce into the boiled broccoli broth and whish it around a little.
Now you need a giant bowl in addition to your pot and a blender. Pour the hot soup into the blender a little at a time and BLEND. This is messy. Dump your florets into the bowl of hot, blended soup, as you blend it, then pour it all back into the pot and boil a little more to soften the florets.
Makes enough soup for me for about 8 servings.