In the bowl of a stand mixer, cream together the butter and the sugar on medium speed until light and fluffy.
Add the vanilla and incorporate into the butter and sugar mixture.
Add the flour and cornstarch. On low speed, mix into the butter and sugar until well incorporated.
Divide the dough into two portions, wrap each portion completely in plastic wrap and store in the fridge for 2 hours.
When ready to bake, remove dough from fridge and let sit at room temperature for a few minutes. Preheat oven to 350 degrees. Prepare a baking sheet by lining it with parchment paper or a silicone liner. Set aside.
Roll one portion of the dough to 1/4 inch thick on a lightly floured surface. Use a star shape, or your favourite cookie cutter shape to cut out the cookies. Transfer to the prepared baking sheet, leaving 2 inches of space between each cookie.
Bake for 15 minutes. Remove from oven and let sit for 2 minutes before transferring to a wire cooling rack to finish cooling.
For the Icing:
Once the cookie is completely cooled, whisk together the icing ingredients and set aside.
Line the cookies up on the cooling rack so that they are evenly spaced. Place a layer of paper towels under the cooling rack for easy clean up. (This will catch the icing if any drips over the side.)
Dip each cookie, top side down, into the icing. Do not submerge the cookie. Just dip the surface. Gently shake off the excess and place the cookie, icing side up, back onto the cooling rack.
Top the cookie with sprinkles and move on to the next cookie until all cookies have been iced and sprinkled.
Allow the iced cookies to sit undisturbed for one hour. This will allow the icing to harden.
Cookies can be stacked. Store in a food-safe container. Can be frozen up to 3 months.
The reason we divide the dough before chilling is so we can limit the amount of contact the dough will have with our warm hands. If the dough warms up too much, the fine lines created by your cookie cutters will not be as precise once the cookie is baked. Also, when re-rolling the cookie dough multiple times after you have cut out the first batch, the dough will become tougher and the cookie will not bake with a smooth surface.