In the bowl of a standing mixer, or if you don't have one, you can use a bowl and a hand mixer, add the butter and sugar. Cream until light and fluffy, scraping down the sides often.
Add the egg, and vanilla extract. Mix until just incorporated, then Add the flour and baking powder.
Wrap the dough in plastic wrap and refrigerate for 1-2 hours
On a lightly floured surface, roll the dough out to a 1/4 inch thickness. lightly flouring a cookie cutter, press into the dough, and carefully transfer cut out to a parchment lined baking sheet. Do this until all the dough is used. Refrigerate again for 15 minutes.
Pre heat the oven to 325 degrees F. Bake for 10-12 minutes or until lightly golden around the edges. Take out of the oven and let stand 5 minutes, then transfer to a wire rack to cool completely.