In with an electric mixer or in the bowl of a stand mixer using the paddle attachment, beat the butter until light and fluffy. Add the granulated sugar and beat until well blended. Beat in the flour, then the chopped and ground walnuts. Remove the dough from the bowl and form into a large disc. Wrap the dough in plastic and chill in the refrigerator for 30 minutes.

Preheat the oven to 325 degrees F.

Remove the chilled dough from the refrigerator. Cut the dough into quarters and then cut each quarter into sixths for a total of 24 equal-size pieces. Roll each piece of dough between your palms into 2-inch balls. Arrange the 24 balls onto 2 parchment-lined baking sheets (12 cookies on each sheet), spacing them 1-inch apart. Bake the cookies until golden brown on the bottom and just pale golden on top, 20 to 25 minutes. Cool the cookies for 5 minutes on the baking sheet. Toss the warm cookies in the powdered sugar. Transfer the sugar-coated cookies to a rack to cool completely. (The cookies can be prepared 2 days ahead. Store them in an airtight container at room temperature.) Sift more powdered sugar over the cookies before serving.