Wash chrysanthemum leaves, sorrel and swiss chard. Remove stems from all the greens and cut out the large rib of the swiss chard. Roughly chop greens and the chives and set aside.
Place butter and oil in a heavy saucepan over medium heat. When butter is melted, add the minced shallots and sauté until softened, about three minutes. Add the greens and peas, stirring to coat with butter and oil. Add a little salt and the water. Cover and simmer for about 8-10 minutes, until peas are tender.
Ladle the soup into a food processor or blender, discarding a ladleful or two of the “broth”, and process until smooth. If desired, strain processed soup before returning to the saucepan. Over low heat, stir soup and add cream and salt and pepper to taste. Serve garnished with chive blossoms and/or croutons.