Heat the butter and olive oil in a large saucepan over low heat. Stir in the garlic, shallots, and ginger, and cook until fragrant but not brown, about 5 minutes. Stir in the green onions, cauliflower, parsnip, and mushrooms, and cook and stir an additional 5 minutes. Add the pear, beans, mustard, and dill, and stir just until heated, about 1 minute.
Stir in the wine and thyme, and turn up the heat to high. Boil, stirring constantly, until the wine is reduced by half and is syrupy, about 5 minutes. Pour in the chicken broth. Return the mixture to a boil, then reduce heat to low and simmer, partly covered, until vegetables are tender, about 20 minutes. Allow the soup to cool slightly.
Pour the soup into a blender, filling the pitcher no more than halfway full. Hold down the lid of the blender with a folded kitchen towel, and carefully start the blender, using a few quick pulses to get the soup moving before leaving it on to puree. Puree in batches until smooth and pour into a clean pot. Alternately, you can use a stick blender and puree the soup right in the cooking pot.
Stir in cream, and, if needed, thin with additional chicken broth; serve hot. You may wish to serve this soup the next day. It will improve in taste with time.
