In a Dutch oven, combine the first six ingredients; bring to a boil. Reduce heat; cover and simmer for 1 hour or until vegetables are tender.
With a potato masher, puree most of the vegetables. For dumplings, combine the egg, water, salt and flour until smooth and stiff. Drop by teaspoonfuls into the boiling soup. Cover and simmer until the dumplings are cooked through, about 10 minutes. Garnish each serving with a butter and parsley.