Process the pistachios and one tablespoon of the flour in a food processor until you have a fine mixture. Do not over process.
In a medium bowl sift the cake flour then mix in the baking powder and chopped pistachios.
In a large bowl, whip the eggs with the sugar until pale yellow and almost triple in volume.
Fold in the flour mixture.
Fold in the melted butter.
Place the bowl in the refrigerator to chill.
Grease a madeleine pan, or a mini cupcakes pan (total 12 cavities) and fill each mold 3/4 full.
Chill for 1-4 hours.
Bake on the middle center for 8-10 minutes, at a 40F preheated oven, until the cookies are puffy with a small bump at the center and a toothpick comes out dry, or with a few moist crumbs from the center of the cookies.
Remove from the oven and allow to chill in the pan for about 12-15 minutes before inverting.