Preheat the oven to 325°F / 165°C.
In a large stand mixer set to medium or a large mixing bowl, whisk the butter and sugar together until light and fluffy.
Add the egg yolks one at a time, while whisking, and add in the milk.
Combine the flour, baking powder, and vanilla sugar in a medium bowl and add this to the mixture, whisking until combined.
Grease a 12 x 16-inch (30/32 x 40 cm) rimmed baking sheet. Cover with a piece of baking parchment.
Gently spread the batter evenly and thinly across the baking sheet.
In a clean, large stand mixer set to medium-low or a large mixing bowl whisk together the egg whites until foamy.
Add the sugar a little at a time and continue to whisk until glossy, stiff peaks form.
Gently pour the meringue evenly over the batter.
Sprinkle the sliced almonds evenly across the meringue.
Place in the middle rack of the oven and bake for 30 minutes, until the meringue is dry and lightly golden.
While the cake is baking, prepare the vanilla custard and whipped cream.
Make the custard by whisking together the sugar and egg yolks in a bowl.
Add the cornstarch and blend until the mixture is pale yellow and thick.
Place the whole milk in a saucepan and add the vanilla beans.
Warm the milk just before it begins to boil, without letting it boil.
Steadily and slowly, add the milk to the bowl with the sugar mixture, whisking constantly.
Pour it back into the saucepan and return to the stove. Cook until it has thickened.
In a large stand mixer set to medium or a large bowl, whisk the heavy cream until soft peaks form.
Fold the whipped cream into the cooled custard.
When the cake has cooled, lift it out with the parchment paper and place on a cutting board.
Cut the cake in half and peel it from the parchment paper.
Gently turn it over on a serving tray so the meringue side is facing downwards.
Spread all of the custard cream over the cake and gently place the remaining half on top, with the meringue side up.
Best to chill for an hour or so before serving.
