Heat the oven to 350°F (175°C), and line baking sheets with parchment paper if desired. Make sure the butter is softened but not melted, since softened butter creams properly and helps the dough hold its shape.

Cream the softened butter and 1/2 cup confectioners’ sugar until smooth and light. Beat in the vanilla extract until it is evenly incorporated.

Gradually add the all-purpose flour, mixing just until a soft dough forms. Stir in the finely chopped walnuts, taking care not to overmix the dough.

Shape the dough into one-inch balls and arrange them about one inch apart on the prepared baking sheets. Keep the balls similar in size so they bake at the same rate.

Bake for 12–15 minutes per batch, or until the bottoms are lightly browned. The tops should remain relatively pale, because overbaking can make these tender cookies dry.

Let the cookies stand briefly, then roll the warm cookies in additional confectioners’ sugar. Allow them to cool completely before rolling them a second time for a thicker, more even coating.