Cheesy Cream of Broccoli Soup

I made a great cream of broccoli soup, following Bittman's How to Cook Everything: Simple Recipes for Great Food. He uses the same basic recipe for cream of nearly any vegetable soup, so feel free to substitute carrots, celery, cauliflower, turnips, etc.

4 cups chicken broth
1 pound (about 4 cups) of vegetable, trimmed and chopped
1/2 cup rice
salt and pepper to taste
1/4 to 1 cup cream or milk
1 cup shredded Cheddar cheese
minced fresh parsley for garnish

I used chicken broth because I had it. You could easily substitute vegetable or beef broth for a different flavor, or even water for a somewhat plainer one. I used the rice for a thickener. His other option is a potato, peeled and quartered. An older recipe I like uses oatmeal.
Combine the broth, vegetables, rice (or potato) and bring to a boil. Turn down and simmer about 15-20 minutes, until the vegetables are very tender. Puree with an immersion blender or food mill or regular blender (let it cool a bit first for anything other than the immersion blender). Taste and add salt and pepper as needed. Add the cream. I used the full cup AND added the Cheddar cheese because I felt like it.

It was awfully tasty!