In the bowl of a stand mixer fitted with the whisk attachment, beat the eggs at medium speed while gradually adding the sugar.
Once all of the sugar has been added, increase the speed to medium-high and continue whipping the mixture until it's very thick and pale in color, about 3 to 4 minutes. Add vanilla and lemon zest and whip for a few seconds.
In a mixing bowl, sift flour and whisk together the baking powder and salt.
Using a silicon spatula, fold in the flour mixture into the egg mixture in three additions, stirring just until combined.
Fold in the melted butter until well combined.
Cover the bowl and refrigerate for at least 1 hour but you can chill up longer for better results.
30 minutes before baking. Preheat the oven to 350° (F) or 170° (C). Generously brush the molds of your madeleine pan with butter so they will not stick.
Using a a spoon or medium cookie scoop, spoon level scoops of the batter into the center of each mold. You don't need to spread the batter, it will spread out by itself and keep a more uniform shape that way.
Bake 8-10 mins until slightly golden around edges and centers look set and slight hump has appeared. Allow to cool slightly and remove from the tin and allow to cool
Dust with powdered sugar and serve with tea or coffee! Bon Appetit!