Heat the butter in a pan and gently fry the shallot until softened but not coloured.
Add the new potatoes and fennel and sauté for 2-3 minutes.
Add the stock and bring to the boil. Reduce the heat and simmer for 8-10 minutes, or until the vegetables are tender. Season, to taste, with salt and freshly ground black pepper and allow to cool slightly.
Pour the soup into a blender, add the dill and blend until smooth. If necessary, gently reheat the soup before serving.
To serve, pour the soup into a serving bowl.