Combine the flour, cornstarch, icing sugar and nuts in a large bowl. (Ideally sift them together). Blend in the butter with a large spoon. Work with your hands until a soft, smooth dough forms.
Shape into 1 inch balls. Place on an ungreased baking sheet about 1 1/2 inches apart. Flatten the balls with a lightly floured fork.
Shape the dough into a smooth roll about 1 1/2 inches in diameter. Wrap and chill until firm (about 4 hours or overnight). The rolls can be stored in the refrigerator for up to 1 month. Cut the roll with a sharp knife into thin slices. Place on an ungreased baking sheet.
Bake at 300ºF for 20-25 minutes or until the edges of the cookies are lightly browned. Remove from the sheet and cool completely before storing.
Dust with icing sugar or ice with frosting. Makes about 36 cookies, depending on size.