Butter a 9-inch cake pan, then line it with parchment paper.
Sift together flour, salt and baking powder onto a piece of parchment or waxed paper.
Using a stand mixer, beat the eggs and vanilla sugar until thick and pale yellow.
Add dry ingredients to the eggs and sugar, alternately with the milk - beginning and ending with the dry ingredients.
Fold in the lemon zest.
Fold in the melted butter.
Pour the batter into the prepared cake pan, and bake in the center of the oven until the cake is golden and slightly puffed, about 30 minutes.
Check after 25 minutes - if cake tester stuck in the center of the cake comes out clean, it is done.
Let cool to room temperature on a wire rack.
Remove cake from the pan, put on a plate or cake stand, and dust with confectioners' sugar.
Notes
To remove the cake from the cake pan, run a knife around the edge of the cake. Place the wire rack on the pan and flip it. Shake firmly and the cake will drop from the pan. Remove the parchment paper and let the cake cool, right side up.