Heat oven to 325 degrees. In a small saucepan, melt butter until light amber in color.Advertisement
Brush madeleine pan with melted butter, and dust lightly with flour. Place hazelnuts and 1 tablespoon confectioners' sugar in the bowl of a food processor fitted with a steel blade, and process until very fine.
Combine hazelnut mixture, 1 cup plus 3 tablespoons confectioners' sugar, flour, and salt in a medium bowl. Add egg whites and vanilla, and whisk to combine. Add melted browned butter, and whisk until incorporated. With a tablespoon, fill molds evenly, about 3/4 of the way. Transfer to oven, and bake 14 to 18 minutes. Cool 2 minutes, and remove from pan. Cool completely on a rack, ridged side up. Dust cookies with confectioners' sugar.