In a medium saucepan, melt 80 grams of butter over medium heat until fully melted, stirring gently. Add 100 ml of milk, 100 ml of water, and ½ teaspoon of salt to the melted butter, mixing until the ingredients combine and reach a gentle simmer for about 3 minutes.

Once the mixture starts to simmer, whisk together 500 grams of flour and 1 teaspoon of baking powder in a separate bowl. Gradually add this dry mixture to the saucepan, stirring continuously until a smooth, cohesive dough forms, resembling a soft ball, about 2 minutes.

Remove the saucepan from the heat and allow the dough to cool for about 5 minutes. Once slightly cooled, add 4 beaten eggs one at a time, mixing thoroughly after each addition until the dough is silky and smooth.

While mixing in the eggs, preheat your oven to 400°F (200°C). Prepare a baking pan by greasing it lightly with butter or lining it with parchment paper.

Divide the dough into two equal portions. Press one half into the prepared baking pan evenly, and place it in the preheated oven. Bake for about 20 minutes or until the top is golden and a toothpick inserted comes out clean. Repeat this process with the second portion of dough.

For the cream filling, whisk 4 eggs with 150 grams of sugar in a saucepan until light and frothy. Incorporate 3 tablespoons of flour and 100 ml of milk, and then cook the mixture over medium heat, stirring constantly for about 5 minutes until thickened.

Remove the cream filling from the heat and allow it to cool for 10 minutes. In a mixing bowl, beat 80 grams of butter until fluffy, then gradually incorporate the cooled cream mixture. Whip until fully combined and smooth.

To assemble, place one layer of the baked dough on a serving platter. Spread half of the cream filling evenly over the layer, then gently position the second layer of dough on top. Spread the remaining cream filling over the top layer.

Refrigerate the assembled cake for at least 2 hours to allow the flavors to meld and the cream to set. Dust the cake with icing sugar before serving.