In a small saucepan heat the milk and ginger over a medium-low heat until scalding, about 4 minutes. While the milk is warming, put cocoa powder and sugar into a mug. Add the water to the mug and stir until the mixture has the consistency of a paste. Remove the ginger from the warmed milk. Add the chocolate mixture to the milk and whisk until slightly frothy. Pour the hot chocolate into the mug and top with chocolate shavings.