How to Make It
In the bowl of a standing electric mixer fitted with the paddle, beat the butter with the sugar at medium speed until fluffy, about 2 minutes. Beat in the egg yolks, vanilla and salt, then beat in the 2 1/2 cups of flour at low speed. Divide the dough in thirds and pat into disks. Wrap each disk in plastic and refrigerate until chilled, about 30 minutes.
Preheat the oven to 350° and line 3 baking sheets with parchment paper. On a lightly floured work surface, roll out one disk of dough inch thick. Using a 3-inch cookie cutter, stamp out cookies as close together as possible and transfer them to a baking sheet 1-inch apart. Bake the cookies in the center of the oven until lightly browned, 18 to 20 minutes. Let cool slightly, then transfer the cookies to a rack to cool completely. Repeat with the remaining disks of dough. Gather and reroll all of the dough scraps; stamp out and bake more cookies.
In a medium bowl, whisk the egg whites until frothy. Add the lemon juice and confectioners' sugar and whisk until smooth. Pour some of the icing into several small bowls and stir in food coloring; cover the bowls with plastic wrap. Add a few drops of water to the white icing to thin it slightly so it will glaze the cookies evenly. Using a pastry brush, coat all of the cookies with the white glaze. Let the glaze dry completely. Transfer the colored icings to piping bags fitted with tiny tips (or to sturdy, small, resealable plastic bags with a tiny bit of a corner snipped off) and pipe designs over the cookies. Let the icing dry completely before serving.