Preheat the oven to 350°F (175°C). Line two baking sheets and a 9 × 13-inch baking dish with parchment paper.

Roll out both puff pastry sheets, place them on the lined baking sheets, and prick them all over with a fork.

For flatter pastry layers, optionally cover each sheet with parchment paper and place another baking sheet on top as a weight.

Bake for 20–22 minutes, until golden and crisp. Remove from the oven and cool completely.

Trim the baked pastry sheets to fit the 9 × 13-inch dish. Place one sheet in the bottom of the dish.

In a saucepan over medium heat, whisk together the milk, heavy cream, butter, vanilla, and sugar. Heat until small bubbles appear around the edge.

Whisk the flour and water together until smooth. Stir this slurry into the hot milk mixture, then remove the saucepan from the heat.

Slowly whisk a little of the hot milk mixture into the beaten egg yolks to temper them. Gradually whisk the tempered yolks back into the saucepan.

Return the saucepan to medium heat. Bring the custard to a boil while whisking constantly, then cook for 30–60 seconds, until thick.

Pour the hot custard over the pastry layer and spread it evenly. Top with the second pastry sheet, trimming and gently pressing it into place.

Refrigerate for 3–4 hours, or until the custard is completely set.

Dust with powdered sugar, slice, and serve chilled.