Put milk into a microwave-safe container and cook on High in the microwave for 2 minutes. Mix in chocolate, sugar, and cinnamon. In a small bowl, whisk an egg until smooth, then mix it into the chocolate mixture.
Return to microwave and cook on High for 3 to 4 minutes or until foamy (be careful not to let it boil.) Remove from the microwave, whisk until smooth and pour into 3 mugs.
Garnish with a sprinkle of cinnamon or more grated chocolate if desired.