If you are making other broccoli dishes in which you really only want the florets, save the stems and use them within the week for this delicious soup. You only need 2 cups of florets to stir in after pureeing, so make up the difference with peeled and chopped stems in the soup. Alternately, just use a big bunch of broccoli, and use up every bit of it.
Peel and chop broccoli stems and onion, reserving the broccoli florets. Put in a big pot, add rice and stock or water. Bring to a boil and reduce to a simmer until vegetables and rice are very tender, about 15 minutes.
Reserve 2 cups of broccoli florets, then add the rest of the florets to the soup and simmer for 5 more minutes. Steam or microwave the remaining 2 cups broccoli florets just until crisp tender.
Puree the broccoli mixture in batches to a smooth consistency, adding sour cream and milk as it becomes smooth.
Return to pan and gently reheat, whisking in just enough milk to thin to a consistency of your liking.
Stir in broccoli florets, salt, pepper and basil. Warm just to serving temperature. Be very careful not to boil.
If you want a heavier ratio of stems: 1 1/4 pound stems and 5 ounces broccoli florets