In a small dish, whisk the cornstarch into 1/2 cup of the milk until completely dissolved and no lumps remain. Set aside.

Heat the remaining milk over medium-low heat until simmering, stirring occasionally to dissolve any skin that forms. When the milk is simmering, remove from the heat and stir in the chocolate. Cover and allow to sit 10 minutes.

Remove the lid and whisk until smooth. Add the brown sugar and the cornstarch mixture and return to low heat. Heat, stirring frequently, until thickened and smooth, about 10 minutes more. Stir in the vanilla and salt and serve!