Preparing the Dough

1. Melt the Butter and Combine Liquids
   In a saucepan, melt 80 grams of butter over medium heat. Add 100 ml each of milk and water, along with ½ teaspoon of salt. Stir the mixture until the butter is fully melted and the liquids are combined.

2. Mix the Dry Ingredients
   In a separate bowl, whisk together the flour and baking powder. This ensures that the baking powder is evenly distributed throughout the flour.

3. Incorporate the Dry Mixture
   Once the liquid mixture comes to a boil, reduce the heat and slowly add the dry mixture, stirring continuously to prevent lumps. Cook the dough until it pulls away from the sides of the pan and forms a smooth ball.

4. Cool and Add Eggs
   Transfer the dough to a mixing bowl and allow it to cool slightly. This step is crucial to prevent the eggs from cooking when added. Once the dough is warm but not hot, add the eggs one at a time, mixing thoroughly after each addition. The dough should be smooth and slightly sticky.

5. Bake the Layers
   Preheat your oven to 400°F (200°C). Line a 25cm round baking pan with parchment paper. Divide the dough into two equal portions. Spread one portion evenly in the pan and bake for 20 minutes on the medium rack. Repeat with the second portion to create two layers. Allow the layers to cool completely before assembling.

Making the Cream Filling

1. Whisk the Base Ingredients
   In a mixing bowl, beat the eggs and sugar until the mixture is pale and frothy. Gradually add the flour, followed by the milk, whisking constantly to create a smooth batter.

2. Cook the Cream Mixture
   Transfer the mixture to a saucepan and cook over medium heat, stirring constantly. As the mixture thickens, continue stirring to prevent lumps. Once it begins to boil, let it cook for three minutes. Remove from heat and cover with plastic wrap to cool.

3. Blend the Butter and Cream
   In a separate bowl, beat the butter until light and fluffy. Gradually add the cooled cream mixture, a few spoonfuls at a time, blending well after each addition. The result should be a smooth, creamy filling.

Assembling the Cake

1. Layer the Cake
   Place one layer of the baked dough in a clean baking pan. Spread half of the cream filling evenly over the surface. Add the second layer of cake on top and spread the remaining cream over it.

2. Chill the Cake
   Refrigerate the cake for at least two hours to allow the cream to set and the flavors to meld.

3. Garnish and Serve
   Before serving, dust the top of the cake with icing sugar or your choice of garnish. Slice and enjoy this delightful dessert with family and friends.