Toast almonds and hazelnuts; cool completely. Place nuts in a food processor; cover and process until finely ground.
In large bowl, beat egg whites on medium speed until soft peaks form. Gradually beat in sugar, 1 tablespoon at a time, on high until stiff glossy peaks form and sugar is dissolved. Combine the nut mixture, flour, cinnamon and nutmeg; fold into egg whites. Cover and refrigerate for 1 hour.
On a lightly floured surface, roll dough to 1/4-in. thickness. Cut with a floured 2-in. star-shaped cookie cutter. Place 1 in. apart on parchment-lined baking sheets.
Bake at 325° until edges are lightly browned, 9-11 minutes. Remove to wire racks to cool. If desired, sprinkle with confectioners' sugar.