Melt the chocolate over a warm bain-marie.
Warm the milk to room temperature, then puree the banana and confectioners' sugar with the milk.
Pour into glasses and add 2-3 teaspoons of the melted chocolate to create swirls of chocolate in the smoothie.
Serve at once.
Tips: Bananas that are a rich yellow with small brown streaks or spots will have the right level of ripeness and the best flavour for this smoothie.