In a mixing bowl, sift together the flour, cornstarch, and salt. Set aside.
In the bowl of a stand mixer, mix together the butter and sugar until light and creamy. Mix in the eggs one at a time until fully incorporated. Mix in the extract.
Slowly add in the flour mixture and mix until just incorporated. The dough will be sticky. Divide the dough in half and wrap each half in plastic wrap and chill for 1 ½ - 2 hours.
On a lightly floured surface, roll out each disk of dough to ¼ inch thickness. Using the cookie cutter, cut out the dough and carefully transfer to a parchment-lined baking sheet. Chill for 20-30 minutes.
Preheat the oven to 375℉.
Bake for 8-9 minutes until the cookies are just set and just starting to lightly brown around the edges. Let cool on pan briefly before transferring to a cooling rack to cool completely.
Icing
Add the powdered sugar and 2 tablespoons milk to a small bowl. Stir together until smooth. Add more milk as necessary to reach desired consistency. The icing should be thin enough to dip the cookies into, but thick enough to coat the cookies.
Divide the icing into three small bowls. To each bowl, add 1-2 drops of food coloring gel. Stir to combine.
Dip the top of each cookie into the icing. Let the excess drip off and place the cookie on a rack placed over a sheet pan. Let dry.
Store the cookies in an airtight container for 2-3 days.
Notes
The number of cookies that this recipe yields will depend on the thickness of the dough when rolled out and the size of the cookie cutter.
Start with room temperature butter and eggs to ensure the ingredients mix together smoothly and evenly.
Don't skip the chill time. I know chilling dough can be a hassle. I get it. But it is an important step to prevent the cookies from spreading and losing their shape during baking.
Change up this recipe for any season - use any seasonal cookie cutter and customize the color of the icing.
For extra flavor in the icing, add maple or vanilla extract.
If you want the icing to dry with more of a sheen, add 2 teaspoons corn syrup.
For a thicker glaze, add more powdered sugar or less milk. For a thinner glaze, add more milk.