In a medium bowl, stir all ingredients until well combined. Try not to overmix.
Flour your surface and rolling pin. Roll out the dough about ½ inch thick. Cut out cookies with your favorite cookie cutters, and place on a baking sheet lined with parchment paper.
Bake cookies for 9-10 minutes. They won't really look any different, maybe slightly brown on the edges, so just trust the timing. Allow to cool before glazing.
While the cookies are cooling, make the glaze. Combine 1 cup powdered sugar, 1 tablespoon vanilla extract, and 1 tablespoon water. Whisk with a fork until there are no lumps.
Dip the tops of cookies into the glaze, letting the excess drip off. Transfer to a wire rack and decorate as desired while the glaze is still soft.
Cookies can be stored in an airtight container for up to 3 days.