Cut the fennel into thin strips; save the fennel greens. Chop the shallot finely.
Heat 2 tablespoons of olive oil in a frying pan. Fry the shallot with the fennel seeds for 1 minute. Add the fennel strips and fry for 2 minutes without browning.
Pour the wine into the pan and braise the fennel gently for 10 minutes.
Meanwhile, heat the mashed potato according to the instructions on the package.
Stir the puree into the fennel. Season with pepper.
Put the fennel puree on a dish or 4 plates. Sprinkle with the preserved fennel green.