In your saucepan, off the heat, mix together the cornstarch, cocoa powder, sugar, and salt.
Stir in just a couple of tablespoons of the milk and mix until the mixture forms a thick paste and there are no clumps.
Turn on the heat to medium and stir in half of the remaining milk and stir to combine.
Add the chopped chocolate.
Continue stirring until the mixture is hot and steaming, but not bubbling.
Remove from the heat and stir in the vanilla.
Top with whipped cream or other preferred toppings.
Notes
You can substitute the brown sugar with granulated sugar or half the amount of sugar substitute such as stevia. You can also replace it with honey or maple syrup, but it will impart a flavor to the drink.
You can use any type of unsweetened milk you prefer.
You can use any type of chocolate chip or plain chocolate bar you like for the drink. If you use milk chocolate, you may need to reduce the amount of sugar you add.