Preheat your oven to 375°F. Lightly grease a madeleine pan with melted butter and dust each mold with a little flour.

In a medium bowl, beat the eggs with vanilla extract and lemon zest using an electric mixer for about 5 minutes until the mixture becomes thick and pale. Slowly add the powdered sugar while beating continuously.

Sift together the all-purpose flour, salt, and baking powder. Gently fold this dry mix into the egg mixture using a rubber spatula until just combined.

Slowly fold in the melted and cooled butter until the batter is smooth. Avoid over-mixing to keep the batter light.

Spoon the batter into the prepared madeleine pan, filling each mold about 3/4 full. Bake for 10 to 12 minutes until the tops are light golden and spring back when lightly touched. Let cool in the pan for 1 minute before transferring to a cooling rack. Dust with powdered sugar if desired and serve warm.