Wash and peel all of the vegetables and the apple. Cut the apple, cucumber, the half beetroot and the celery in to small brunoise cubes. Chop the dill and zest the lime.
Mix the cream with the white balsamic vinegar, dill, lime zest and the chopped vegetables. Season with salt and piment d'Espelette then set aside in a cool place.
Preheat the oven to 200°C.
Cut the brick pastry sheets to shape using a pastry cutter and brush with melted butter. Make stacks of pastry 3 layers thick and sprinkle with sesame seeds. Make 3 stacks of 3-layered pastry per person. Place on a baking tray, cover with a second tray to stop them from rising and then bake in the oven for 4 to 6 minutes.
Cut the smoked halibut in to strips. Make the mille-feuille by spreading one layer of pastry with the vegetables and cream, top with a second layer of pastry. Place some strips of smoked fish on this layer and finish with a third layer of pastry.
Place the quarter beetroot, water and the white balsamic vinegar in blender and mix.
Serve the mille-feuille with the vinaigrette and a few sprigs of fresh dill.
«Depending on the types of pastry cutter you have, cut the pastry in to squares, rectangles or circles...»