In the bowl of your mixer cream butter and sugar until smooth, at least 3 minutes
Beat in egg and vanilla extract.
In a separate bowl combine baking powder and salt with flour and add a little at a time to the wet ingredients. The dough will be very stiff. Wet your hands and finish off kneading the dough by hand.
There is no need to chill this dough, you can just begin working with it. Divide into workable batches, roll out onto a floured surface and cut. You want these cookies to be on the thicker side (closer to 1/4 inch rather than 1/8).
Bake at 350 for 6-8 minutes. Let cool on the cookie sheet until firm enough to transfer to a cooling rack.