1. Preheat your oven to 375°F (190°C). Grease a 9-inch square baking pan and set it aside.

2. In a large bowl, combine the flour, 1/2 cup of softened butter, 1/2 cup of granulated sugar, baking powder, and salt. Using a pastry cutter or your fingers, mix the ingredients until they resemble coarse crumbs.

3. Gradually add 2 of the eggs, one at a time, mixing well after each addition. The dough should come together into a smooth ball.

4. Divide the dough in half and roll each half into a rectangle that fits the prepared baking pan. Carefully transfer the dough rectangles to the pan, pressing them into the bottom and up the sides to create a crust.

5. In a medium saucepan, whisk together the milk, cornstarch, and 1/2 cup of granulated sugar. Cook over medium heat, stirring constantly, until the mixture thickens and comes to a boil. Remove from heat and stir in the vanilla.

6. Separate the remaining 2 eggs, placing the yolks in a small bowl and the whites in a clean, dry bowl.

7. Beat the egg yolks lightly, then slowly pour in the hot milk mixture, whisking constantly. Return the mixture to the saucepan and cook over medium heat, stirring continuously, until the custard thickens, about 5 minutes.

8. Remove the custard from the heat and let it cool slightly. Pour the custard into the prepared crust, smoothing the top with a spatula.

9. In a clean bowl, beat the egg whites with an electric mixer until stiff peaks form. Gently fold the beaten egg whites into the remaining 1/2 cup of softened butter.

10. Spread the whipped butter mixture over the top of the custard, making sure to cover it completely.

11. Bake the Karpatka Cake for 30-35 minutes, or until the top is golden brown.

12. Remove the cake from the oven and let it cool completely in the pan. Dust the top with powdered sugar before serving.