In the bowl of an electric mixer, cream together the butter and sugar until light and fluffy.
Add the egg and vanilla, and mix until combined.
In a separate bowl, whisk together the flour, baking powder, and salt.
With the mixer on low speed, add the flour mixture to the butter mixture, and mix until just combined.
Divide the dough into two equal pieces, wrap each in plastic wrap, and refrigerate for at least 1 hour or up to 2 days.
When ready to bake, preheat oven to 375°F (190°C). Roll out the dough on a lightly floured surface to 1/4-inch (6 mm) thickness, and cut out desired shapes using cookie cutters.
Place the cut-out cookies on baking sheets lined with parchment paper or silicone baking mats, and bake for 8-10 minutes, or until just golden brown around the edges.
Remove from the oven, and let cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
Interesting Facts
This dough can be made in advance and stored in the refrigerator for up to two days before baking.
You can use any type of cookie cutter to make your cookies.
For best results, chill your cookie dough before rolling it out.