Wash the rice under cold running water and drain well.
Dissolve the cocoa powder in 4 tablespoons of the milk.
Place the remaining milk, the cinnamon stick and the dissolved cocoa in a heavy-based saucepan. Bring to boiling point then pour in the rice in a stream. Cover and cook gently for around 25 minutes.
Add the brown sugar, blend well, cover and cook for a further 5 minutes. Remove the cinnamon stick.
Divide the chocolate rice pudding among small serving bowls and allow to cool slightly.