Put the milk on the fire. Add vanilla and break the chocolate into slices. Fire on medium heat. Stir the milk so that the chocolate does not burn.
Mash the banana into a puree and add it to the milk. Continue to heat the milk and stir. When the bubbles appear, remove the milk from the heat. Do not bring to a boil.
Pour the milk back into the blender bowl and whisk for 15 seconds. When serving, if desired, the top can be sprinkled with ground cinnamon. You can drink a cocktail hot or warm.