Add the eggs, vanilla, and salt; continue blending until combined. Slowly add the flour, mixing just until combined. Be careful not to overmix! Cool for 1 hour.
While baking, prepare the icing by combining the confectioners sugar, milk, and corn syrup in a small bowl. Adjust the milk measurement as needed to reach your desired consistency. Squeeze a small amount of food coloring into the icing and use a toothpick to swirl it around for the marbled effect.
Once the cookies are done cooking and have fully cooled, dip each one into the icing face down. Lift them up and allow the excess to drip off. Add icing or edible glitter, if desired.