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Wash and trim about 2 or so pounds of broccoli- keep in mind if you plan to cook they way I do and not use the woody stems you will need a little over 2 pounds of broccoli. Cook in boiling salted water until tender (about 5 minutes). Drain Broccoli reserving 2 cups of the broccoli cooking water. Chop broccoli, set aside. Hopefully you'll have 3 to 4 cups of broccoli.
Pour broth and cooking water into a 4 quart pot. Bring to a boil and add celery, onion parsley, and rice. return to a boil, then lower heat and simmer for about 20 minutes or until rice is cooked. Add 3 cups of the broccoli and simmer for 5 minutes longer. Soup should be getting thick by this point. Puree broccoli with your immersion blender or put in a food processor. be careful as it is HOT! After you're done pureeing the soup, add in the half and half and butter, add in the rest of the broccoli if you desire and chunky soup or puree all of it for a nice creamy soup (I do it both ways depending upon my mood). Add salt and pepper to taste and serve it with a thick slice of a crusty whole grain bread.