Clean and wash the fennel, cut off the fennel greens and cut the fennel bulb into slices. Simmer in boiling salted water for about 5 minutes. Pour onto a sieve, rinse with cold water and drain well. Chop the fennel green finely. Mix vinegar, salt, pepper, mustard and sugar, add half of the oil and stir in half of the fennel greens.
Heat the rest of the oil in a frying pan and fry the Rösti corners in it on each side over medium heat for about 4 minutes. Clean the salad, wash and pat dry. Drain the olives. Arrange the lettuce leaves, fennel, olives and one Rösti corner each on four plates, pour the marinade over them and sprinkle the remaining fennel greens over them. Sprinkle the salad with pepper and serve garnished with basil