Prepare the Puff Pastry: Preheat the oven to 400°F. Line a baking sheet with parchment paper. Place the puff pastry on a lightly floured surface and gently roll it into an even rectangle. Prick the pastry all over with a fork to help control excessive puffing.
Bake the Pastry: Place the puff pastry on the prepared baking sheet. Cover it with parchment paper and place another baking sheet on top to gently weigh it down. Bake for about 20–25 minutes, or until the pastry is deeply golden and crisp. Remove the top baking sheet and parchment during the final few minutes if needed for additional browning.
Cool and Cut the Pastry: Transfer the baked pastry to a wire rack and allow it to cool completely. Using a serrated knife, carefully trim the edges and cut the pastry into even rectangular layers. Reserve the pastry scraps for decorating the finished cake.
Make the Vanilla Pastry Cream: Warm the milk in a saucepan over medium heat until steaming but not boiling. In a separate bowl, whisk together the egg yolks, granulated sugar, cornstarch, and salt. Slowly whisk the warm milk into the egg mixture, then return everything to the saucepan. Cook over medium heat, whisking constantly, until the mixture becomes thick and smooth.
Finish and Chill the Pastry Cream: Remove the pastry cream from the heat and stir in the butter and vanilla extract. Transfer it to a clean bowl and press plastic wrap directly against the surface. Refrigerate until completely chilled and thickened.
Add the First Layer of Pastry Cream: Place one cooled puff pastry layer on a serving board or platter. Spread an even layer of chilled vanilla pastry cream over the pastry, using an offset spatula to create a smooth surface.
Build the Napoleon Cake: Place another pastry layer gently over the cream. Continue alternating pastry layers and vanilla pastry cream until all the layers have been used. Press very gently as you assemble the cake so the delicate pastry remains intact.
Decorate the Cake: Finish with the final pastry layer. Sprinkle the top generously with crushed baked pastry crumbs and powdered sugar. Use the reserved pastry scraps to create a rustic, bakery-style finish.
Chill and Slice: Refrigerate the assembled Napoleon Cake for at least 4 hours so the layers can settle and the pastry cream can firm up. When ready to serve, use a sharp serrated knife and gently saw through the layers to create clean slices.