Peel and chop the shallots. Peel, wash and cut the potatoes into small pieces. Clean and wash the fennel. Cut 4-8 fine slices from 1 tuber for decoration. Cut the rest of the fennel into small pieces. Heat butter in a pot. Sauté shallots, potatoes, pieces of fennel and fennel seeds in it while stirring. Add wine and 600 ml broth. Bring to the boil, cover and cook for about 20 minutes until soft.
Preheat oven (electric cooker: 180 °C/circulating air: 160 °C/gas: see manufacturer). Cut the duck breast crosswise on the skin side, but do not cut into the meat. Place in a cold pan with the skin side down. Fry at medium heat for approx. 8 minutes until golden brown. Turn the fillet and fry on the meat side for about 2 minutes. Season with salt and pepper and place in an ovenproof dish with the skin side up. Cook in a hot oven for 8-10 minutes. Remove from the oven, cover and leave to rest for about 5 minutes.
Roughly chop the nuts. Cut duck breast into thin slices. Finely puree the soup, mix in the cream and possibly add some stock to the desired consistency. Season to taste with salt and pepper and pour through a fine sieve. Arrange the fennel slices, duck breast and nuts in soup bowls, sprinkle the fennel greens on top. Drizzle with olive oil as desired.