Place the milk and cinnamon in a medium saucepan and bring to a simmer over medium-low heat. Remove from heat and set aside for 10 minutes to develop the flavours.
Place the cocoa powder in a small heatproof bowl. Add 80ml (1/3 cup) of the warm milk mixture and stir until a smooth paste forms.
Remove the cinnamon sticks from the remaining milk mixture and place saucepan over low heat. Add the cocoa paste and chocolate, and use a wire balloon whisk to stir for 5 minutes or until chocolate melts and the mixture is well combined.
Transfer to a heatproof serving jug and pour into heatproof glasses to serve.