Sift together the confectioners’ sugar, almond flour, cake flour, nutmeg, and cardamom. Place the sifted ingredients in the bowl of an electric mixer fitted with the whisk attachment. On the lowest speed, add the egg whites; mix until all the dry ingredients are moistened. Increase the speed to medium and beat until very smooth. Decrease the speed to low and stir in the browned butter, then increase the speed to medium and beat until smooth.