Start by heating a pot of water to a gentle simmer for a double boiler. At the same time, preheat the oven to 400°F and line an 18x13-inch jelly roll pan with parchment paper, buttering it lightly.

In a metal bowl, whisk together the eggs, egg yolks, sugar, and salt. Set the bowl over the simmering water and whisk until the mixture reaches about 100°F.

Transfer the mixture to a stand mixer and beat for about 5 minutes until it triples in volume and thick, pale ribbons fall from the whisk.

Sift the cake flour and cornstarch together, then fold them gently into the egg mixture until no flour streaks remain.

Spread the batter evenly in the prepared pan and bake for 7 to 10 minutes until a knife inserted in the center comes out clean. Let the sponge cool completely.

Split the vanilla bean and scrape the seeds into a saucepan. Add cream and sugar, whisk in the egg yolk, and cook over low heat until thickened. Let it cool.

Blend the cooled custard with chestnut puree until very smooth, then strain through a fine double-mesh strainer.

In a separate bowl, whip the heavy cream to soft peaks, add powdered sugar, and fold in the strained chestnut puree until firm peaks form.

Trim the cooled sponge, then cut it into 8 rectangles. Pipe the chestnut cream in layers on each rectangle.

Finish with a strand of strained puree on top and serve soon after assembling for the best texture.