1. Preheat your oven to 400°F (200°C).

2. In a large bowl, combine the flour, chilled butter, water, and salt. Use a pastry cutter or your fingertips to work the butter into the flour until the mixture resembles coarse crumbs.

3. Turn the dough out onto a lightly floured surface and knead it briefly until it comes together into a smooth ball. Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.

4. In a medium saucepan, whisk together the eggs, sugar, milk, and cornstarch. Cook over medium heat, stirring constantly, until the mixture thickens and comes to a boil, about 5-7 minutes.

5. Remove the saucepan from the heat and stir in the vanilla extract. Pour the pastry cream into a clean bowl and cover the surface with plastic wrap to prevent a skin from forming. Refrigerate for at least 2 hours, or until completely chilled.

6. Once the dough has chilled, roll it out on a lightly floured surface into a large rectangle, about 1/8-inch thick. Cut the dough into 6 equal-sized rectangles.

7. Place the dough rectangles on a parchment-lined baking sheet and bake for 15-20 minutes, or until the pastry is golden brown and puffed.

8. Remove the baked pastry layers from the oven and let them cool completely on a wire rack.

9. Assemble the Karpatka Cake by placing one layer of pastry on a serving plate. Spread a generous amount of the chilled pastry cream over the top. Repeat with the remaining pastry layers and pastry cream, creating a multi-layered cake.

10. Dust the top of the Karpatka Cake with powdered sugar before serving.