Preheat the oven to 375 degrees.
In a medium bowl combine the flour and baking powder.
In the bowl of a stand mixer, fitted with the paddle attachment, beat the butter and both sugars at medium speed until smooth. Beat in the egg and vanilla until combined.
With the mixer at low speed gradually add the flour mixture. You may need to stop and scrape the sides of the bowl throughout. Beat until the mixture is all incorporated and pulls away from the side of the bowl to create a ball around the paddle.
Wrap the dough in plastic wrap and refrigerator for 10 minutes.
Lightly flour your work surface and roll out the dough out until it's about 1/4-inch thick. Using your selected cookie cutter, cut out the shapes and transfer the cookies to a non-stick cookie sheet placing 1-inch apart. Roll up the remaining scraps and repeat.
Bake the cookies for about 8 minutes. The cookies should be nice and fluffy and light in color. You do NOT want the cookies to start to brown around the edges. Let the cookies cool a few minutes before transferring to a wire rack to cool completely before frosting.