Lightly grease a 16- or 24-cavity madeleine pan with melted butter, then lightly dust with flour to prevent sticking (or using a baking spray).
In a medium bowl, whisk together the flour and baking powder (to combine and aerate).
In a separate medium-sized mixing bowl, beat the first measure of sugar together with the eggs for several minutes, until the mixture is light yellow and very thick.
Add the melted-then-cooled butter and vanilla, and beat for another few minutes. The batter should be quite voluminous.
Gently fold in the flour mix, so the batter loses as little volume as possible.
Portion the batter into the lightly greased wells of a standard-size madeleine pan, using 1.5 tablespoons of batter for each well. Freeze the pan+batter (covered or uncovered), for 2-3 hours. If you have extra batter remaining, cover & refrigerate the batter.