Preheat oven to 180 degrees C (350 degrees F).
Combine eggs and sugar in a bowl. Mix until slightly golden in color.
Add vanilla sugar, flour, cocoa powder, baking powder, milk and melted butter, alternating between liquid and solid, while mixing with a hand mixer (or stand mixer).
Line a 9 x 13 rectangular cake pan with a baking sheet. Pour cake mixture on the lined cake pan.
Place in the lower part of the oven, for 35 to 40 minutes.
Take the cake out of the oven and set aside to cool.
In a bowl, combine butter, espresso, cocoa powder, vanilla sugar and powdered sugar. Mix.
Using a spatula, spread the icing evenly on top of the cooled cake.
Sprinkle the dried coconut on top of the icing.
Refrigerate for at least 30 minutes to chill the icing.
Cut cake into squares. Serve.