(Nutrition information is calculated using an ingredient database and should be considered an estimate.)
Sift flour, cornstarch and salt in a large bowl, whisk together.
Using a handheld or stand mixer, cream together butter and sugar until light and fluffy. Add in the eggs one at a time, incorporating fully. Scrape bowl if needed. Mix in vanilla extract and add dry ingredients from step 1.
Roll out dough between two pieces of parchment paper to about 1/3 to 1/2 inch - this is a thicker cookie! (Making them too thin will cause them to brown too much around the edges.) Chill until firm; then cut out cookies and reroll/chill scraps for more.
Bake at 350F for about 9 minutes, or until edges just slightly start to brown. Turn pan halfway through baking.
Sift icing sugar, mix in corn syrup and extract. Add 4-5tbsp milk - don't add too much! It will not seem like enough liquid but keep whisking and it will come together. The ideal consistency should be running slowly off the whisk.
Separate into bowls and add food colour as desired. Place into piping bags. Decorate cooled cookies; if flooding, try outlining the cookie first then letting it set before flooding to prevent the icing from slipping off. Use a toothpick to manipulate icing.