In a food processor combine almonds, pistachios, and 1/2 cup of the powdered sugar. Cover and process until nuts are very finely ground but still dry (not oily). Add 1 1/2 cups of the powdered sugar, the flour, orange peel, lemon peel, baking powder, and salt. Cover and pulse with on/off turns to combine; set aside.
In a large bowl beat egg whites, almond extract, and vanilla with an electric mixer on medium speed until soft peaks form (tips curl). Gradually add the remaining 1/2 cup powdered sugar, beating until medium-stiff peaks form (tips stand almost straight). Gently fold the nut mixture into the egg white mixture until the mixture forms a dough.
Line a shallow baking pan with plastic wrap. With damp hands, or using a rubber scraper, form dough into a 12x6-inch rectangle. Wrap dough in plastic wrap. Chill overnight in the refrigerator.
Preheat oven to 350 degrees F. Line a cookie sheet with parchment paper or foil. Unwrap dough. Using a long sharp knife, cut dough into 2x2-inch squares. Cut each square in half diagonally to form two triangles. Place 1 inch apart on prepared cookie sheet.
Bake in the preheated oven for 10 to 12 minutes or until bottoms are light brown. Transfer to a wire rack. Sift additional powdered sugar over warm cookies. Cool completely.