Mix sugar, cocoa and 2 tablespoons cold milk in a mug until smooth. Heat the remaining milk in a small saucepan on the stovetop or in a 2-cup glass measure in the microwave until steaming hot but not boiling. Stir in the cocoa mixture and vanilla.
To froth the hot chocolate, whirl a whisk in it by rubbing your hands back and forth. (Alternatively, pour the hot chocolate into a blender, cover with the lid and a kitchen towel and blend until frothy.) Pour it back into the mug and sprinkle with cinnamon.