Preheat oven to 350° F. Line 2 baking sheets with parchment paper or silicone baking mats.
Place butter in a bowl; sift confectioners' sugar over it; add the salt. On low speed, beat just until smooth, but not fluffy. You want a homogeneous dough, but you don't want to beat air into it. Beat in the egg white. This will make the dough separate and it will be slick and slidey. Keep mixing for about 1 minute. Don't be concerned if the mixture curdles; the flour will smooth it out. Beat in the vanilla and scrape down the bowl. Gradually add the flour, beating only until it disappears into the soft dough.
Fit a pastry bag with an open-star tip, one that's a scant ½-inch in diameter. Trasnfer the dough into the piping bag.
Pipe the dough onto the lined baking sheets in tight "W" shapes that are about 2-inches wide and 1½-inches high, leaving about 2-inches of space between them - the dough will puff and spread while baking. You can make the cookies larger or smaller or in different shapes, but whatever you do, leave enough space between them to spread out.
Bake the cookies for 17 to 20 minutes, rotating the pan at the midway point. The cookies should be golden brown at their edges and on their bottoms and paler at the center. Allow the cookies to cool on the baking sheets for a few minutes, then transfer them to racks to cool at room temperature.
Dust with confectioners' sugar if you'd like, just before serving. Yield: 24 cookies.
Notes
Packed airtight, the cookies will keep for at least 1 week; they can be frozen for up to 2 months. If you decide to freeze them, it's best not to dust them with confectioners' sugar.