Melt the butter in either in your microwave or in a small pot over medium heat. Once melted, pour the butter into a bowl and allow it to cool to room temperature.
In a medium bowl, sift together the flour, baking powder and salt. Whisk it together and set aside.
In the bowl of a stand mixer fitted with a whisk attachment (or in a large bowl using a handheld mixer), combine the eggs and sugar. Beat on high speed for 4 to 5 minutes until the mixture is a very pale yellow color with a thick silky texture. (This may take closer to 5 to 7 minutes with a handheld mixer.) When you lift the beaters, the mixture will leave thick ribbons on the surface when it’s ready. Mix in the vanilla and lemon zest on low speed just until combined.
Fold the dry ingredients into the egg mixture and mix until just combined. (You can sift the flour mixture into the eggs while you fold to avoid getting lumps or over-mixing the delicate batter.)
Drizzle the butter into the batter and gently mix until just combined.
Cover and refrigerate the batter for 1 hour.
Spray inside the cavities of the Madeleine pans with nonstick baking spray. (Alternatively, you can brush them 1 tablespoon of melted butter). Refrigerate the pans for about 1 hour while the batter is chilling.
After the batter has chilled for 40 minutes, preheat the oven to 350°F.
Scoop a generous tablespoon of batter into each of the scallop-shaped wells. Bake for 8 to 10 minutes until golden brown on top and the cakes spring back slightly when pressed with your finger.
Let the madeleines cool in the pan for about 3 minutes, then turn out of the pan to cool completely (not on the scalloped side.)
Serve with a light dusting of powdered sugar.
Video
Notes
Brown the butter for a lovely depth of flavor. See my tutorial for how to brown butter if you are unfamiliar with the process. If you decide to use browned butter, I recommend browning a full stick (8 tablespoons) and then measuring out 7 tablespoons for the recipe. This is because some moisture will evaporate from the butter during browning, and the volume will be reduced when it is finished.
Measure your flour correctly! Adding too much flour to the recipe is a common mistake, which will yield dry madeleines. The best and easiest way to measure flour is by using a scale. If you don't have one, fluff your flour with a spoon, sprinkle it into your measuring cup, and use a knife to level it off.
Use room-temperature eggs. Set the eggs out in advance so they are not very cold when you start preparing the batter. Room-temperature eggs are easier to whip up and aerate.
The batter is delicate. The madeleine batter is a genoise batter, which means it gets most of its lift from tiny air bubbles beaten into the eggs. So be gentle with your delicate batter to avoid it deflating. In step 4, when you add the flour mixture to the wet ingredients, you can sift the flour mixture into the eggs while you gently fold to avoid over-mixing the batter.
Chill the batter before baking. This shock in temperature (cold batter in a hot oven) helps the little sponge cakes puff up and create their signature hump.