Line two baking sheets with parchment.
Beat the room temperature butter (soft, not melted) on medium high for 4 to 5 minutes, until pale and fluffy.
Add the powdered sugar and vanilla and beat until smooth.
Add the flour a little at a time, mixing just until a soft, pliable dough forms.
Chill the dough until it is firm enough to roll without sticking to your fingers: 15 to 20 minutes in the fridge or 6 to 8 minutes in the freezer.
Heat the oven to 300°F with a rack in the middle.
Scoop about 1 tablespoon of dough per cookie. Roll each piece into a 5 to 6 inch rope about as thick as your pinky.
Curl one end toward the center and the other end the opposite way to make an S. Place on the lined sheets about 1 inch apart.
Chill the shaped cookies in the fridge for 10 minutes so they hold their S shape.
Bake one sheet at a time on the middle rack for 17 to 18 minutes, until the tops look dry and pale and the bottoms are just slightly golden. They will still be soft.
Let the cookies cool on the sheet. Do not move them until they have cooled; they firm up as they cool.
About 5 minutes after they come out of the oven, sift ¼ cup powdered sugar over the warm cookies. Right before serving, dust with the remaining ¼ cup.