Preheat oven to 425°F. Prepare two baking sheets by covering them with parchment paper.
Lightly dust a working surface with flour. Place a puff pastry sheet on the surface and roll as thin as you can, maintaining a square or rectangular shape. Repeat with the second sheet.
Place each puff pastry sheet on the prepared baking sheet. Place one baking sheet on top of the other. Place a third baking sheet on top of the top baking sheet - this is to prevent the pastry from rising too much. Bake until golden, about 18 minutes. Remove and set aside to cool, placing a dish on top of the pastry to prevent it from puffing up.
Meanwhile, prepare the pastry cream.
Place the milk and 1/2 Tbsp sugar in a medium saucepan. Scrape the vanilla beam into the milk, mix and throw the rest of the beam in it. Heat over medium heat until it starts to simmer, then cover, turn heat to low and let simmer for 30 minutes.
Meanwhile, place the remaining sugar in a medium mixing bowl. Add the eggs to the bowl with sugar and whisk until pale yellow. Add the cornstarch and whisk again.
Remove the vanilla beam from the milk and gradually whisk the milk into the egg mixture. Return the custard to the saucepan and heat over medium-low heat, whisking constantly until the custard starts to thicken, about 5 minutes. Continue whisking until you notice bubbles - then whisk for another minute and remove from heat.
Add the butter to the custard and continue whisking until it's melted and incorporated. Transfer to a bowl. Cover with plastic wrap, pressing down on the custard, to avoid a film forming. Refrigerate until cold.
Meanwhile, remove stems from strawberries. Half or thickly slice two cartons worth of berries. Set aside.
Once the custard is cold, add the heavy cream to the custard and mix until combined.
Cut each puff layer sheet into thirds.
Assembly the pastries. Place a layer of puff pastry in a serving plate. Place custard in a pastry bag and pipe custard onto the puff pastry. Cover with sliced strawberries. Add another layer of puff pastry and repeat. Add a final layer of pastry, dust with powdered sugar and decorate with whole strawberries.
