Preheat the oven to 325°F. Line two baking sheets with parchment paper or silicone mats; set aside. In the large bowl of a stand mixer fitted with the paddle attachment, combine the flour, softened butter, and powdered sugar. Mix on low speed initially (so that the flour and sugar don't come out of the bowl), and then gradually increase to medium speed. Mix until completely combined and a soft dough forms. The mixture will look dry and crumbly at first, but let the mixer keep running for a few minutes and the dough will eventually form into a soft ball.
Roll out the dough on a lightly-floured surface (to about ¼-inch thickness, or slightly thicker).
Use cookie cutters, biscuit cutters, or a sharp knife to cut out desired shapes. Place the shapes on the prepared baking sheets.
Pierce each cookie a couple of times with the tines of a fork.
Bake for 20 minutes, or until just starting to turn lightly brown on the edges. Do not overbake or the cookies can become dry and hard. Let the cookies cool on the pan for 5 minutes, and then transfer to a wire rack to cool completely.