Melt 80 grams of butter in a medium saucepan over low heat. Pour in 100 ml of milk, 100 ml of water, and ½ teaspoon of salt. Increase heat to medium and bring to a boil. Whisk in 150 grams of flour and 1 teaspoon of baking powder until cohesive, about 2-3 minutes.

Allow the dough to cool for about 5 minutes. Crack 2 eggs into a bowl and add one at a time to the dough, stirring vigorously after each addition. This should take around 3-4 minutes.

Preheat oven to 400°F (200°C) and grease a round cake pan. Spread half of the dough evenly into the pan and bake for about 20 minutes until golden. Cool on a wire rack and repeat with remaining dough.

For the creamy filling, beat 2 eggs with 100 grams of sugar in a mixing bowl until frothy, about 5 minutes. Gradually mix in 40 grams of flour and 100 ml of milk, stirring continuously. Transfer to a saucepan and cook over medium heat until thickened, about 5-7 minutes.

Once thickened, let the cream cool slightly. Beat 80 grams of softened butter until light and fluffy, then gradually add the cooled cream mixture, blending well.

On a serving platter, place one baked cake layer and spread half of the cream filling evenly over it. Layer the second cake on top and spread remaining filling over it. Smooth with a spatula.

Cover the cake with plastic wrap and refrigerate for at least 2 hours to set the cream.

Dust the top with icing sugar before serving, slice, and enjoy.