Shift the cocoa and sugar together into a medium-sized saucepan.
Dissolve the cornstarch in the water, and stir into the cocoa and sugar until it is a smooth paste.
Begin heating the mixture, stirring it with a whisk, and gradually pour in the milk.
Continue stirring with the whisk as you bring the liquid to a simmer.
Allow the chocolate to simmer for about 10 minutes, stirring often, until it is thick, glossy and completely smooth.
Serve steaming hot in coffee mug.