Preheat the oven to 180°C (350°F). Line a 25/35 cm (10x14 inches) baking tray with parchment paper.
In a bowl, combine the flour with the ground walnuts, vanilla sugar, and baking powder.
Mix the butter with the sugar until it becomes creamy (5-10 minutes). Add alternately a whole egg and a tablespoon of flour. Mix well and repeat until you have added the 4 whole eggs. Add the remaining dry ingredients.
Whisk the egg whites with a pinch of salt. Gently fold the egg whites into the egg and buttercream with upward movements. Pour the mixture into the baking tray and smooth it out.
Bake for 30-35 minutes. After passing the toothpick test, transfer to a cooling rack.
When completely cooled, cut the cake vertically into two smaller pieces of 25/17 cm (10x6.5 inches). Cut each piece horizontally into 2 thinner pieces. This will give four 25/17cm (10x6.5 inches) sized pieces.
Caramel cream:
Add the sugar together with the water in a small thick-bottomed saucepan. Allow the sugar to melt and boil until it turns a deep copper color. Turn off the heat and add the butter. Stir vigorously to homogenize the mixture. Add the milk and mix well. Leave the mixture on low heat.
Whisk the egg yolks gently. Slowly pour the caramel cream over the yolks. Return the mixture to the stove and leave it over a low heat. Stir continuously until the cream begins to thicken. It will take about 8-10 minutes (on low heat). Turn off the heat.
Hydrate the gelatin in cold water. After 5 minutes, drain it and add it to the warm cream. Mix well. Stir the cream every 10 minutes until completely cooled.
Mix the whipping cream with a tablespoon of vanilla sugar until firm. Incorporate the whipped cream into the caramel with upward movements.
Chocolate Icing:
Hydrate the gelatin in cold water.
Place the whipping cream, water, sugar, and syrup over a medium heat. When the syrup is completely smooth, add the broken chocolate pieces. Stir until the chocolate is melted. Turn off the heat. The icing should not boil.
Add the gelatin and stir well. Let the icing cool and harden. It will be ready to use after 2-3 hours.
Assembly:
Place one of the cake pieces on a platter. Spread a third of the caramel cream (cooled) on top. Continue layering with the cake, cream, cake, cream, cake. Refrigerate for 1-2 hours.
Remove the cake from the fridge and cut into rectangles. Place them on a baking rack. Glaze each rectangle with chocolate icing. Transfer the pieces to a platter and refrigerate, allowing the icing to set.
When serving, decorate the cake with pieces of caramelized sugar.