Combine milk, cocoa powder, and brown sugar in a medium sauce pot on the stove. Whisk together well.
Heat over medium heat, whisking often, until the mixture is steaming and tiny bubbles appear around the edges. Do not boil.
Turn the heat to low and add the chopped chocolate, stirring until melted completely.
Remove from heat and add vanilla extract and salt. Serve immediately with whipped cream and/or marshmallows, if desired.