Lightly grease (or line with parchment) two baking sheets. Preheat the oven to 350°F (for drop cookies; if you're making cutout cookies, wait to preheat the oven)., Beat the butter and sugar together until fluffy. Add the egg and vanilla stir until combined, scraping the sides of the bowl and stirring again briefly., Add the dry ingredients, stirring just until the dough comes together., To make drop cookies: Drop the dough by teaspoonfuls (a teaspoon cookie scoop works well here) onto the prepared baking sheets, leaving about 1 1/2" between them. Bake the cookies for about 12 minutes; they won't brown, but will feel set. Remove them from the oven, and cool completely on the pan., To make cutout cookies: Scoop the dough out onto a piece of plastic wrap, flatten it into a disk, and wrap. Refrigerate the dough for at least 1 hour., Preheat your oven to 350°F. Remove the dough from the refrigerator, and dust your work surface and dough with cornstarch or gluten-free flour., Roll the dough about 1/4" thick and cut the shapes of your choice with a cookie cutter. Place cutouts on a parchment-lined baking sheet and chill for 10 minutes. Re-chill any dough scraps before rolling., Bake the cookies for 8 to 10 minutes. Remove them from the oven, and cool completely before icing.