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.
