Rub the salmon with 2 tbsp coarse salt, 1 tbsp sugar and chopped fennel greens. Then place in a bowl, cover with plastic wrap and refrigerate for at least 8 hours.
Remove salmon from marinade and grate. Then cut into 16 fine slices. Clean fennel, cut into slices and roast in butter-oil mixture for 2 min on each side in frying pan. Roll out 4 slices of brioche bread with a rolling pin, then cut out a circle in the center of each with a cookie cutter (O 7 cm). In a coated frying pan, toast both the bread slice and the cut-out circle. Then layer the fennel slices alternately with the salmon slices (4 per person), finishing with the bread slice and the cut-out circle.
Garnish with fennel greens and dill of choice. Mash 3 tbsp. mayo with a bunch of dill and serve one fennel millefeuille each with a tiny bit of dill mayonnaise.