1Beat butter in large bowl until light. Beat in 1/2 cup confectioner's sugar and vanilla. Add flour and mix until just blended. Stir in nuts. Shape dough into a ball, then flatten into a disc. Wrap in plastic wrap and refrigerate until cold.
2Preheat oven to 325 degrees F (170 degrees C). Line cookie sheets with parchment paper.
3Shape dough into 1 inch balls. Place on prepared sheets, spacing evenly. Bake about 20 minutes, or until firm and lightly colored.
4Sift 1/4 cup confectioners' sugar into a bowl. Transfer cookies to confectioners' sugar while still warm and roll gently to coat. Immediately transfer cookies to plastic bag and seal (this makes the cookies sweat and form an icing). Let stand 5 minutes in the bag. Transfer to rack and cool.