Melt the butter either in your microwave or in a small pot over medium heat. Browning the butter will add a lovely depth or flavor to the cakes but is of course optional. Once melted or browned pour the butter into a bowl and allow to cool.
Sift the flour, salt, and baking powder into a bowl then whisk together and set aside.
Add the eggs and sugar to the bowl or your stand mixer fitted with a whisk attachment or a large bowl if using an electric hand mixer. Beat on high until the mixture is a light yellow color with a thick silky texture, about 8-9 minutes. You'll see the beater leave trails when it's ready. Mix in the vanilla and lemon zest toward the end.
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 chill the batter as well as the buttered tins for 1 hour then scoop one tablespoon of batter into each scallop-shaped well. Bake at 350F 8-10 minutes.
Serve with a light dusting of powdered sugar.
Measure your flour correctly! Adding too much flour to the recipe is the most common mistake. The best, and easiest way to measure flour is by using a scale. If you don't have one then fluff your flour with a spoon, sprinkle it into your measuring cup, and use a knife to level it off.
The batter for these Madeleines is a Genoise, which gets most of it's lift from the tiny air bubbles beaten into the eggs. Be gentle with your delicate batter.
These Madeleines are light and airy cakes, not cookies. They're best the day of but if you're storing leftovers make sure to seal in an airtight container.
If your cakes are sticking in the pan after baking run a knife around the edge and gently press at the base to nudge the madeleine forward. It should release without loosing any crumbs.
Your madeleines will still be scrumptious even if you don't have that characteristic hump on the backnso don't stress about it.