In a 2 quart saucepan with a lid, combine the chocolate and water. Bring to a simmer over medium heat, stirring to melt the chocolate. Whisk in 1⅓cups of the milk and heat until steaming for about 8 minutes, make sure not to boil the mixture.
In a small bowl, stir together the remaining ⅓cup milk and cornstarch until dissolved. Pour into the steaming milk and whisk constantly until the mixture thickens slightly, about 4~5 minutes.
Cornstarch is cooked when the chocolate does not taste chalky anymore and it has a smooth texture.
Turn off the heat and cover the pan.
When ready to serve, whisk the chocolate and pour into cups. Serve with warm churros.