Begin by bringing 6 cups of water to boil together with the cinnamon stick and the chopped piloncillo. Leave it to simmer for 10 minutes, or until the piloncilo has melted. If you are using sugar, it should only take about 5 minutes.
Once the sweetener has dissolved, add the two chocolate bars and melt them in the pot, stirring often.
While the chocolate is melting, mix the cornflour and the remaining 2 cups of water by hand until you achieve a creamy texture.
When the chocolate mixture has become homogenous, slowly pour in the cornflour through a strainer to avoid any lumps. Stir the mixture with a hand mixer to combine the ingredients well.
Increase the heat to medium-high until the champurrado begins to boil, then reduce the heat and allow it to simmer. Stir constantly to avoid burning the champurrado.
After 6 to 8 minutes the mixture should begin to thicken. Cook it for a further 5 minutes.
Turn off the heat and serve. Be careful! The thick consistency of the champurrado keeps the drink extremely hot!