Patricia's Viennese Crescents

Using a small, sharp knife, split the vanilla bean lengthwise and scrape the seeds into a small bowl. Discard the pod. Add 1 tablespoon confectioners' sugar and use a mortar or the back of a spoon to pound and mix them together. Add the remaining confectioners' sugar and stir to combine. Cover and let stand at least 1 hour. DO AHEAD: Vanilla sugar can be made ahead and stored, in an airtight container at room temperature, indefinitely.
Position a rack in the upper third of the oven and a second rack in the lower third then preheat to 350°F.
Using a food processor, grind the walnuts into a chunky paste then transfer to the bowl of a stand mixer fitted with the paddle attachment. Add the butter and sugar and beat on medium speed, scraping the bowl occasionally, until completely incorporated, about 2 minutes. Add the flour in 3 batches and stir until a smooth dough forms, about 2 minutes.
On a lightly floured surface, shape heaping tablespoons of dough into 3- to 4-inch-long ropes, tapering the ends. Curve each rope into a crescent shape. Transfer to a baking sheet, leaving about 2 inches between cookies. Bake, switching the cookies between the upper and lower racks about halfway through baking, until light golden brown, 18 to 20 minutes. Let the cookies cool 2 to 3 minutes then carefully roll them in vanilla sugar and place on racks to cool completely. Continue baking cookies on cooled baking sheets. DO AHEAD: The cookies can be baked ahead and stored, in an airtight container at room temperature, up to 3 days.