Special equipment: madeleine molds
Preheat the oven to 350 degrees F. Butter the madeleine molds and dust them with flour.
Add the flour and baking powder to a medium bowl and whisk well.
Add the eggs and the salt in the bowl of a stand mixer with a whisk attachment and whip at high speed until they triple in volume, about 3 minutes. Pour in the sugar and then the vanilla seeds. Continue beating for a few moments, and then add the lemon zest and juice Slow down the mixer to medium-low and gradually add the flour mixture. When all the flour has been incorporated, add the melted butter.
As soon as the butter has been absorbed by the mixture, turn off the mixer and pour the batter into a large measuring cup. Pour the batter into the molds, filling each mold two-thirds of the way full.
Bake the madeleines until the edges are golden brown, 13 to 14 minutes. Remove from the oven and unmold immediately. Cool on racks and dust with powdered sugar.