Preheat the oven to 200°C (400°F). Line a baking sheet with parchment paper.
Roll out the puff pastry and cut it into 6 equal rectangles. Place them on the baking sheet and prick the surface with a fork to prevent puffing. Bake for 15-20 minutes until golden and crisp. Let cool.
For the pastry cream, heat the milk in a saucepan until warm. In a separate bowl, whisk egg yolks, sugar, and cornstarch until smooth. Gradually add the warm milk to the egg mixture, whisking constantly.
Return the mixture to the saucepan and cook over medium heat, stirring, until thickened. Remove from heat, stir in vanilla, and let cool completely.
To assemble, spread pastry cream over one puff pastry layer. Top with another layer and repeat, ending with a puff pastry layer on top.
For the glaze, mix powdered sugar and milk until smooth. Spread over the top layer. If desired, draw lines with cocoa glaze and create a feathered pattern using a toothpick.
Chill for 1 hour before serving.