For the border icing:
In a small bowl, use a fork to beat together all the ingredients except the food coloring. Beat in the food coloring, a few drops at a time, until colored to your liking. The mixture should be very thick but still pourable.
Transfer the border icing to a squeeze bottle using a funnel. You can also scoop into a pastry bag fitted with a small plain tip. Before you begin icing any cookies, take a few moments to practice on a piece of parchment paper to get the feel of the icing.
Holding the bottle or bag tip directly over one corner of a cookie, begin tracing an outline of the cookie, squeezing gently and using both hands if needed to maintain consistent pressure. I prefer to allow a little slack in my icing line as I go. If you mess up, simply wipe the icing off and start again. Allow the icing to dry slightly before continuing with the flood icing.
For the flood icing:
In a small bowl, use a fork to beat together all the ingredients except the food coloring. Beat in the food coloring, a few drops at a time, until colored to your liking. The mixture should still be pretty thick, but will drizzle more freely than the border icing. If needed, add additional water or milk to loosen until the consistency is pourable. Pour the flood icing into a squeeze bottle or into a pastry bag fitted with a small plain tip.
Prepare as many batches and colors of flood icing as you need to decorate your cookies.
Begin filling the interior of the border drawn on each cookie with the flood icing, being careful not to add too much that it overflows the border icing. Use either the nose of the bottle or a small toothpick to push the icing evenly over the cookie and up against the corners.
Leave the iced cookie to dry for 24 hours. The cookies are dry when the surface is completely smooth, dry, and resists smudging when touched. Store the dried cookies between sheets of parchment paper in an airtight container at room temperature for up to 10 days.