Line 2 baking sheets with parchment. Using an electric mixer, beat the butter and granulated sugar on medium-high until light and fluffy, 2 to 3 minutes. Beat in the egg, then the vanilla and salt.
Reduce mixer speed to low and gradually add the flour, mixing until just combined (do not overmix). Shape into a 1-inch-thick disk, wrap in plastic wrap, and refrigerate for at least 2 hours and up to 3 days.
Heat oven to 350° F. On a floured surface, roll the dough ¼ inch thick. Using lightly floured 2- to 3-inch cookie cutters, cut the dough into shapes, flouring the cutters and rerolling the scraps as necessary. Place 1 inch apart on the prepared baking sheets. Sprinkle with decorating sugar, if using.
Bake, rotating the baking sheets halfway through, until the edges just begin to brown, 12 to 15 minutes. Let cool slightly on the baking sheets, then transfer to a wire rack to cool completely.