In a glass bowl, stir together the cram and sour cream and set aside.
In a dutch oven, saute together cauliflower, onion, shallots and garlic in lemon juice and butter until onions and cauliflower are soft. Do not allow the vegetables to brown. In a food processor or in a blender (in batches) puree the cauliflower mixture with some of the broth.
Pour blended soup back into the dutch oven and add the remaining chicken broth, seasonings, parsley and some of the and chives. Simmer soup for a few minutes. Add the cream mixture and stir until it is blended. Heat through and serve with a sprinkling of chives and dill.