Curling Cock Special Share definition Flag When when one or more men wrap the female's hair around their cock, simulating a curling iron, and then jams it down said female's throat. Man, she came in for a haircut, but I had to give her the Curling Cock Special. Curling Cock Special by BrianMccaleb February 20, 2017 Get the Curling Cock Special mug.