Preheat oven to 325°F with a rack in the center.

Cut the butter into small pieces and place it in a large bowl (or the bowl of a stand mixer) with the sugar. Beat on medium speed until lightened in color and fluffy. Add the vanilla extract and beat to incorporate.

Add the flour and stir in gently with a spatula or wooden spoon until incorporated. I like to mix the last little bit with my hands. Don't overmix, or the cookies will be less tender.

Shape dough into a disk.

Dust work surface and rolling pin with flour and gently roll dough into a ¼-inch thick circle(-ish). Cut into shapes using a cookie cutter. You can re-roll any scraps and use them to make a few more cookies.

Transfer cookies to a cookie sheet lined with parchment and chill in the fridge for 15 minutes to help them retain their shape in the oven.

Bake about 15 minutes, until very lightly golden. (Cookies this thick may not color much at all.)

Remove from the oven and transfer cookies to a wire rack to cool completely before decorating.