Break the chocolate into chunks and set aside. In a small bowl, add 1 or 2 teaspoons of the milk to the cornstarch and mix to form a paste and set aside.
Place the rest of the milk in a small saucepan and warm over a medium-low heat until it is almost boiling then remove from the heat.
Add the chocolate to the warm milk, off the heat, and stir until it has all dissolved. Add the cornstarch paste and stir through well. Taste the mixture and add a little sugar, to taste (or none if you prefer less sweet). Return the pan to the heat but on a very low setting.
Warm the mixture for around 2-5 minutes, stirring constantly, until the mixture thickens. Make sure it doesn't boil. Pour into a cup or cups and serve, traditionally with churros (or at least a spoon!).
Notes
I'd recommend using chocolate that is good quality and around 60-75% cacao. You can use darker, but may need to increase the sugar as it will be more bitter.This hot chocolate is very rich and so while they will be small portions, this is probably best divided into 2 rather than one larger cup. If you know how much sugar you want to add, eg if you've made before, then you can add it to the milk at the start so it dissolved more easily as the milk warms.