Beat butter and 1 cup confectioners' sugar together in a bowl until light and fluffy. Stir in flour and walnuts until dough is just-combined. Roll dough into 1-inch balls and place 2-inches apart on a baking sheet.
Bake in the preheated oven until lightly browned on the bottom, about 10 minutes.
Pour 1/2 cup confectioners' sugar in a shallow bowl. Roll hot cookies in confectioners' sugar to coat; cool cookies completely and roll again in confectioners' sugar to coat.