Preheat oven to 350 °F (180 °C).
Prepare the chocolate sponge cake batter according to the recipe.
Spread out to 12×18 in (30×45 cm) on a baking sheet lined with parchment paper and bake for 15–20 minutes.
Remove from oven, overturn onto a baking tray or cloth dusted with confectioner’s sugar, and carefully remove the paper from the bottom of the cake.
Raise the oven temperature to 430 °F (220 °C).
Prepare the choux pastry batter according to the recipe.
Using a piping bag fitted with a round nozzle, pipe ¾in (2 cm) strips on a baking sheet lined with parchment paper.
Bake briefly at 430 °F (220 °C) then lower to 350 °F (180 °C) and bake for 15–20 minutes.
Remove from oven and let cool.
For the vanilla cream, warm the pastry cream.
Add cold water to the gelatin, remove excess and dissolve in the pastry cream.
Season with a splash of Cointreau, beat until cold, and then fold in the whipped cream.
Fill the choux strips with cream by cutting them the long way, pulling them open, and filling with cream.
Close them again and chill.
For the chocolate mousse, melt the couverture chocolate.
Beat the eggs until creamy and mix in the chocolate, simple syrup, and heavy cream.
Add cold water to the gelatin, remove excess water, and dissolve in slightly warmed rum.
Stir into the chocolate mixture and fold in the whipped cream.
Place the cake base in a baking frame or deep cake pan.
Spread some chocolate mousse on top.
Place the filled choux strips, cover with the rest of the chocolate mousse, smooth, and chill.
Before cutting, dust with sifted cocoa powder and garnish with chocolate flakes.