Pastry Cream:
Slice the vanilla bean down the middle and scrape out the seeds.
Transfer milk and vanilla seeds to a medium pot and heat over medium-high until boiling. Remove from heat and set aside for 15 minutes.
Whisk sugar and cornstarch in a bowl; add egg yolks and whisk until fluffy.
Whisk in 1/4 cup of hot milk mixture, then the rest, and return all to the saucepan.
Cook over medium-high heat, whisking until thick. Remove from heat, stir in butter, and set to cool slightly.
Cover with plastic wrap directly on the surface and chill for at least 2 hours.
Pastry Layers:
Thaw puff pastry for 45 minutes, roll out, and cut into 2×4 inch rectangles.
Bake at 400F on a lined sheet for 11 minutes, covering with another sheet. Cool on a rack.
Glaze:
Mix powdered sugar with vanilla and milk to a spreadable consistency.
Split some glaze for the chocolate version, adding cocoa and additional milk.
Fill piping bags and prepare for assembly.
Assembly:
Layer pastry rectangles with vanilla icing, add chocolate stripes, and create chevrons.
Whip cream with sugar, combine with pastry cream, and layer between pastry sheets.