Place walnuts on a baking tray and toast them in the oven for 15 - 20 minutes. Remove from the oven, coarsely chop and set aside
Combine the remaining ingredients in a large bowl. Transfer half of the mixture to a blender or food processer and puree. Continue with another half. Return puree to the bowl, combining with unprocessed ingredients. Mix in reserved walnuts.
Cover the soup and refrigerate for at least 4 hours before serving it.