Bake the sugar cookies according to the instructions on the package (or bake your own from scratch). Cool completely, for about 3-5 hours.
Once the cookies are completely cooled, whisk the egg whites in a large bowl. Use a hand mixer to blend in the powdered sugar until the icing reaches a thick consistency, about the texture of toothpaste.
Scoop approximately 1 cup of the stiff icing into a piping bag. Pipe a thin line around the edges of the cookies. Allow it to dry.
While the icing is setting, gradually add water, one teaspoon at a time, to the remaining icing until it becomes runny and merges back into itself in less than five seconds. To test this, dip a spoon into the icing and pull it out. The icing should flow off the spoon slowly and smoothly and should 'dissolve' back into the bowl of icing within five seconds.
Transfer the runny icing to a squeeze bottle or another piping bag. Fill the centers of the cookies, which are already lined with now-hardened icing. Use a toothpick to swirl the icing to release any air pockets. Gently tap the cookies on the counter to level the icing. Let the cookies dry completely for about 5-6 hours.
Once the icing is completely dry, heat the water, sugar, and corn syrup to 300-310°F in a skillet. Stir constantly to prevent the sugar from burning and discoloring. When the mixture reaches 300°F, mix in the red food coloring gel. Once it hits exactly 310°F, remove it quickly from the heat.
Immediately use a spoon to splatter, drip, and drizzle the red sugar glaze over the cookies, leaving some areas white for added effect. Let the glaze cool until it hardens, approximately 30 minutes to an hour. Serve the cookies at your next Halloween party or other creepy event. Enjoy!