These feline-shaped treats are inspired by the 1973 short film "How to Draw a Cat".
Sift flour, baking powder, and salt into a large bowl; set aside. Put butter and sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until pale and fluffy. Mix in eggs and vanilla. Reduce speed to low. Gradually mix in flour mixture. Divide dough in half; flatten each half into a disk. Wrap each in plastic. Refrigerate until firm, at least 1 hour (or overnight).
Preheat oven to 325 degrees, with racks in upper and lower thirds. Let 1 disk of dough stand at room temperature just until soft enough to roll, about 10 minutes. Roll out dough on a lightly floured work surface to just under 1/4 inch thick, adding more flour as needed to keep dough from sticking. Cut out cookies with a 4-inch cat-shape cookie cutter, transferring cookies to parchment-lined baking sheets as you work. Roll out the scraps, and repeat. Repeat with remaining disk of dough. Chill cookies in freezer until very firm, about 15 minutes.
Bake cookies, switching positions of sheets and rotating halfway through, until edges turn golden, 15 to 18 minutes. Let cool on sheets on wire racks.