Preheat oven to 325°F (163°C). In a mixing bowl or the bowl of a stand mixer, cream the butter with the powdered sugar until the mixture is light and smooth. In a separate bowl, combine the flour with the finely chopped nuts. Gradually incorporate the dry mixture into the creamed butter, stirring until a cohesive dough forms. Shape the dough into small, even-sized balls and arrange them on an ungreased baking sheet. Bake for 20 to 25 minutes or until the cookies take on a light golden hue. While still warm, roll each cookie gently in a prepared bowl of powdered sugar to coat. Transfer to a wire rack and allow to cool completely.