Trim 3 inches from bottom of broccoli stalks and discard. Separate the tiny flower heads from remaining stalks, (you are going to cook the stalks and florets separately) making sure you break the florets into little pieces. Bring 2 quarts of water to a boil with 1 tablespoon of salt. Drop the broccoli stalks into the boiling water and cook them for about 15 minutes or until tender. Drain well. Meanwhile, steam florets over water for 3 to 4 minutes or until tender but still bright green; remove them from the heat, and keep warm off heat until serving time.
In a food processor puree cooked stalks with butter, cream, salt and pepper to taste. Pat the steamed florets dry, fold half of them into the broccoli puree and spoon it into a serving bowl. "Float" remaining steamed florets on top of puree, flower side up.