Sift the cake flour, baking powder and salt into a medium bowl; set aside. Beat the butter and sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 5 minutes. Add the egg and vanilla and beat until combined. Reduce the mixer speed to low and beat in the flour mixture in two batches until just combined. Divide the dough between 2 pieces of plastic wrap; shape into disks. Wrap and refrigerate until firm, at least 1 hour. (The dough can be frozen for up to 1 month; thaw overnight in the refrigerator before rolling.)
Line 2 baking sheets with parchment paper. Working with 1 disk at a time, roll out the dough on a floured surface, dusting with flour as needed, until about 1/8 inch thick. Cut out shapes with 2- to 4-inch leaf cookie cutters; arrange 2 inches apart on the prepared baking sheets. (If the dough becomes too soft as you work, return to the refrigerator until firm.) Gather the scraps and refrigerate until firm; reroll once to cut out more cookies. Chill the cutouts 30 minutes.
Position racks in the upper and lower thirds of the oven and preheat to 350˚. Bake, switching the pans halfway through, until the cookies are slightly puffed and just slightly golden on the edge, 13 to 15 minutes. Let cool 5 minutes on the baking sheets, then transfer to racks to cool completely before decorating.