Place 1/4 cup of sugar and the vanilla bean in a food processor fitted with a metal blade. Pulse to chop the bean, then add walnuts. Pulse again until finely chopped.
Remove from food processor.
Add the butter and flour.
Mix until well blended.
Pinch off 1 inch square pieces of dough and shape into balls. Shape the balls into crescents, about 2 inches long.
Place about 1/2 inch apart on cookie sheets.
Bake for 10 minutes, then reduce oven temperature to 300 degrees F and bake for additional 10 to 15 minutes, until cookies are dry.