In the bowl of a stand mixer, combine eggs, sugar, lemon zest and vanilla
Whisk on med-high speed for 5 minutes, until mixture is thick and fluffy
Sift the flour, baking powder and salt over the egg mixture, then beat on low, until just combined
Gently fold in the melted butter
Cover and refrigerate mixture for at least an hour
While mixture is chilling, heat oven to 180° celsius
With the extra butter and flour, carefully grease the madeleine pan, getting into every crease. Sprinkle the pan with the extra flour, tipping the pan to ensure each surface is evenly coated. Tap the excess flour out
Once mixture has chilled, scoop a large teaspoon full of mixture into each of the 12 cavities. No need to spread the mixture -it will spread as it cooks
Bake for 8-10 minutes, until lightly golden and springy
Remove from oven and allow to cool in pan for 10 minutes, before gently loosening and releasing each madeleine from the pan.
Allow to cool on a cake rack, then dust with extra icing sugar and serve