In a medium bowl, stir together the sifted powdered sugar, 2 tablespoons of the milk, light corn syrup, and vanilla extract with a spoon until combined.

Check the icing consistency; it should be thick but pipeable, able to hold an outline while still settling into a smooth surface when filled in.

If the icing is too thick, add more milk about 1 teaspoon at a time, stirring well after each addition, until it reaches the right consistency; you may not need the full 4 tablespoons.

If the icing becomes too thin, stir in more powdered sugar until it comes back together.

Divide the icing into small bowls if using different colors, then add gel food coloring a little at a time and stir until you get the shade you want.

Transfer each color of icing to a piping bag fitted with a piping tip, outline each cooled sugar cookie, fill in the center with more icing, and use a toothpick to nudge icing into corners or pop air bubbles.

Add sprinkles, candies, or decorative sugar right away before the icing starts to set so the toppings stick.

Let the decorated cookies sit in a single layer until the icing hardens; the top may feel dry after a couple of hours, but for stacking or storing, let them harden several hours or overnight, and allow up to 24 hours in humid conditions.