In a bowl, mix the flour, baking powder, and salt. Set aside.
Using an electric mixer, cream the eggs, vanilla extract, and sugar until the mixture becomes pale.
Add the dry ingredients, then the melted butter.

Cover the bowl and refrigerate for at least 3 hours (or up to 2 days)

Drop the dough by spoonfuls into the madeleine molds and bake for 11 to 13 minutes in a preheated oven at 400 F (200 C).
Unmold and let cool on a rack, then dust with powdered sugar.
Can be stored for about 2 months in an airtight container.