Mix the eggs with milk and flour to a smooth dough. Season with salt and pepper and let rest briefly. Meanwhile, for the lime cream, wash the lime hot, dry well and finely grate the peel. Squeeze the lime, mix the juice and zest with crème fraîche until smooth. Season to taste with salt and pepper. Now bake 6 paper-thin crêpes. To do this, heat about 1/2 tsp. clarified butter in a coated pan (Ø approx. 24 cm ), pour some batter into the center with a ladle and swirl the pan so that the batter runs into a paper-thin crêpe. Once the crêpe is lightly browned on the bottom and almost set on top, carefully flip with a palette and bake again for about 1 minute until the second side is lightly browned as well. Lift out and keep warm wrapped in aluminum foil. Bake the remaining 5 crêpes in the same way. Then spread 5 crêpes each with the lime cream, top with smoked salmon and carefully layer on top of each other. Finish with the sixth crêpe. Cut the cake into pieces and arrange on plates. Finally, garnish with dill tips.