In a medium bowl, sift together flour, cornstarch, baking powder, and salt. Set aside.
Using an electric mixer, beat the butter at medium speed until light and fluffy, for about 3 minutes. Add sugar and beat until fluffy, about 4 minutes
Mix in the vanilla until incorporated.
Slowly add the dry ingredients to the butter mixture on low speed until combined. Be sure to scrape down the
Shape the dough into a thick disk, wrap it in plastic, and refrigerate for 1 hour.
Preheat the oven to 325°F. Roll out the chilled dough ¼ inch thick on parchment paper dusted with flour and confectioners' sugar. Cut shapes using cookie cutters and place them on a parchment-lined baking sheet.
Bake for 10–12 minutes, until the edges start to turn a very light, pale golden. Cool on a wire rack before decorating.
Wait until they cool, then make the glaze.
Add the glaze ingredients into a medium bowl and whisk with a fork until smooth.
Dip each cookie face-down into the glaze, pull it straight up, and let the excess drip off for a second before placing it on a cooling rack to set. To keep things tidy, lay parchment paper under the rack to catch any drips!
Decorate each cookie as you go since the glaze will harden.