Place the chocolate and half of the milk in a pan and heat on low. When the chocolate has melted, dissolve the cornstarch in the remaining milk and whisk into the chocolate with the sugar. Cook on low heat, whisking constantly, until the chocolate is thickened, about 5 minutes. Add extra cornstarch if it does not start to thicken after 5 minutes. Remove and whisk smooth.
Pour and serve in cups for dipping churros.