Put the sugar, corn starch and potato starch (or rice flour) in a bowl and stir together. Then stir in the cocoa. Add a little of the cold milk to the mixture and stir until smooth. Stir well with a whisk to avoid the formation of lumps.
Put the rest of the milk in a saucepan and add the sugar, cocoa and starch mixture over medium heat. Stir constantly, heat slowly to almost boiling point and allow to thicken.
Add the chocolate chopped into small pieces, stir with a spoon and melt. You can also let the chocolate melt in a water bath beforehand. Do not let the mixture get too hot so that the cioccolata does not burn.