Preheat the oven to 400°F (200°C). Cut the puff pastry into three equal rectangular sheets.
Place the pastry sheets on a baking sheet lined with parchment paper. Dock the pastry with a fork (pierce it all over) and bake for 10-12 minutes, or until golden brown. Let cool completely.
Meanwhile, prepare the vanilla cream: Bring the milk to a simmer with the seeds scraped from the vanilla bean. Remove from the heat and let cool slightly.
In a bowl, whisk together the egg yolks, sugar, and cornstarch until smooth. Gradually whisk in the warm vanilla-infused milk.
Return the mixture to the saucepan and cook over medium heat, whisking constantly, until the cream thickens. Let cool completely.
Whip the heavy cream to stiff peaks. Gently fold the whipped cream into the cooled vanilla cream until light and airy.
Assemble the millefoglie: Place one pastry sheet on a serving plate. Spread with a layer of vanilla cream. Repeat the layering until all the pastry and cream are used.
Top with the final pastry sheet and dust generously with powdered sugar.
Refrigerate the cake for at least one hour to allow the layers to set. Slice and serve chilled.
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