In a saucepan, heat the milk, water, sugar, salt, and butter until the butter is completely melted.
Remove from the heat and add all the flour, stirring vigorously until a ball of dough forms.
Return to the heat and cook for a few minutes, stirring constantly, until the mixture begins to pull away from the sides of the pan. Let cool slightly, then add the eggs one at a time, mixing well after each addition, until smooth and uniform.
Cook the batter:
Preheat the oven to 230°C (450°F).
Spread the batter onto a 45×35 cm baking sheet lined with parchment paper, smoothing it with a spatula.
Bake at 230°C (450°F) for 10 minutes, then reduce the temperature to 200°C (400°F) and bake for another 10 minutes, or until golden brown.
Let cool completely.
Prepare the filling:
In a saucepan, heat the milk with the vanilla pod (halved and scraped out).
In a bowl, combine the custard powder, egg yolks, and sugar.
Pour the yolk mixture into the hot milk, stirring constantly until the custard thickens. Remove from the heat and let cool completely.
Cream the butter at room temperature and add it to the cooled pudding, mixing until smooth.
Assemble the cake:
Cut the cooked cake in half horizontally.
Spread a layer of cream on the bottom of the cake and cover with half of the sliced strawberries.
Place the other half of the cake on top and spread another layer of cream.
Decorate with the remaining strawberries and sprinkle with powdered sugar.
