Preheat your oven to 400°F (200°C). Roll out the puff pastry sheets to fit an 8x8-inch baking pan. Prick the pastry with a fork to prevent bubbling, then bake for 10-12 minutes until golden and crisp. Let cool completely, then trim edges.

In a medium saucepan, heat whole milk and heavy cream over medium heat until steaming. In a bowl, whisk remaining milk, sugar, egg yolks, cornstarch, and flour until smooth. Slowly add hot milk mixture to temper egg yolks, then return to saucepan and cook for 3-5 minutes until thickened. Stir in butter and vanilla until glossy.

Line a square pan with parchment paper. Place one layer of baked puff pastry at the bottom, pour custard over it, spreading evenly. Add the second layer of puff pastry on top. Cover with plastic wrap and refrigerate for at least 2 hours.

After chilling, lift the dessert out of the pan using parchment overhang. Slice into squares and dust with powdered sugar before serving.