Beat 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.

Preheat the oven to 325 degrees F (170 degrees C). Line cookie sheets with parchment paper.

Shape chilled dough into 1-inch balls. Place on the prepared sheets, spacing evenly.

Bake in the preheated oven until firm and lightly colored, about 20 minutes.

Sift 1/4 cup confectioners’ sugar into a bowl. Transfer warm cookies to confectioners’ sugar and roll gently to coat. Immediately transfer cookies to a resealable plastic bag, seal the bag, and let sit until cookies sweat and form an icing, about 5 minutes. Transfer to a wire rack and cool.