Heat the oven to 400 F. Roll the puff pastry into a rectangle, place it on parchment, prick it all over, and chill for 15 minutes.
Cover with a second sheet of parchment and another baking sheet to keep it flat. Bake for 15 minutes, remove the top sheet, and bake 8 to 10 minutes more until deeply golden. Cool completely.
Cut the pastry into three equal rectangles with a serrated knife.
Make the Pastry Cream:
Warm the milk in a saucepan until steaming. Whisk the sugar, egg yolks, and cornstarch in a bowl until smooth.
Slowly whisk the hot milk into the egg mixture, return it to the saucepan, and cook over medium heat while whisking until thick and bubbling.
Remove from the heat and whisk in the butter and vanilla. Press plastic wrap directly on the surface and chill until cold.
Assemble and Glaze:
Place one pastry rectangle on a board and spread with half of the pastry cream. Add a second pastry rectangle and the remaining cream, then finish with the third rectangle.
Stir the powdered sugar with the water to make a thick glaze. Spread it over the top pastry layer.
Pipe thin lines of melted chocolate across the glaze and drag a toothpick through them to create a feathered pattern. Chill for 1 hour before slicing.
Notes
Bake the pastry until fully golden so it stays crisp after assembly.
A chilled pastry cream makes stacking much easier.
Use a hot, dry knife and wipe it between cuts for cleaner slices.