In a bowl, combine half the milk, the sugar, cocoa, cornflour and vanilla. Mix until smooth.
Put the rest of the milk in a heavy bottomed saucepan with the butter and bring to a boil.
Stirring constantly, add the milk/cocoa mixture to the saucepan and continue to stir until it simmers. Cook over low heat, stirring, until it thickens to the consistence of thick cream.
Pour into a heatproof bowl and set aside to cool. Lay a sheet of plastic wrap over the surface so it doesn't form a skin. Refrigerate about 30 minutes.
When cold, stir in the chocolate. Pour into ice block molds and put in the sticks. You can also use yogurt cups and plastic spoons for the sticks. Freeze overnight.