1. Chop the vanilla bean. Pound it in a mortar or pulverize it in an electric blender with about one tablespoon of the sugar. Mix with the remaining confectioners' sugar. Cover and let stand, preferably overnight. Reserve while cookies are baked.

2. Preheat the oven to moderate (350 F).

3. Cut the walnuts with a sharp knife into very small pieces. Pound the pieces to a paste, using a mortar and pestle.

4. With a wooden spoon or the fingers, mix the walnuts, butter, granulated sugar and flour to a smooth dough. Shape the dough, about a teaspoon at a time, into small crescents, about one and one-half inches in diameter.

5. Bake on an ungreased cookie sheet until slightly browned, or 15 to 18 minutes. Cool one minute. While still warm, roll the cookies in the prepared vanilla sugar.