Preheat oven to 350°F (180°C). Grease and flour a 9-inch (22 cm) cake pan.
Separate the eggs. In a clean bowl, whisk the egg whites with a pinch of salt until stiff peaks form.
In a separate bowl, cream the egg yolks with the granulated sugar and vanilla sugar until light and fluffy. Add the melted butter and milk and mix well.
In another bowl, combine the flour, baking powder, and grated lemon zest.
Gradually add the dry ingredients to the egg yolk mixture, mixing until just combined. Gently fold in the whisked egg whites to keep the batter light and airy.
Pour the batter into the prepared cake pan and spread evenly with a spatula.
Bake in the preheated oven for approximately 35-40 minutes, or until golden brown and a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool completely before slicing it in half horizontally.
Prepare the vanilla cream: cook the vanilla pudding powder with the heavy cream until it thickens into a dense cream. Let it cool completely.
Spread the cooled vanilla cream evenly over the bottom layer of the cake, then carefully place the top layer on top.
Dust the top of the cake with powdered sugar, or decorate with a lemon glaze.
Refrigerate for at least 1 hour before serving to allow the flavors to meld.
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