This variation on our Classic Shortbread got their name either from their likeness to frilly underskirts or a mispronunciation of the French petites gatelles (little cakes).
Preheat oven to 300 degrees, with rack in upper third. Sift flour and salt into a bowl; set aside. Put butter into the bowl of an electric mixer fitted with the paddle attachment. Mix on medium-high speed until fluffy, 3 to 5 minutes, scraping down sides of bowl. Gradually add sugar; beat until pale and fluffy, about 2 minutes.
Reduce speed to low. Add flour mixture all at once; mix until just combined.
Using plastic wrap, press dough into a buttered 10-inch fluted tart pan with a removable bottom. With plastic on dough, refrigerate 20 minutes.
Cut out a round from center using a 2 1/4-inch cookie cutter; discard. Put cutter back in center. Cut dough into 8 wedges; prick all over with a wooden skewer. Refrigerate 20 minutes.
Sift 1 tablespoon granulated sugar over top. Bake until golden brown and firm in center, about 1 hour. Transfer pan to a wire rack. Recut shortbread into wedges; let cool completely in pan. Can be stored in an airtight container up to 2 weeks.