Combine the milk, heavy cream, sugar, cocoa powder and a pinch of salt in a medium saucepan. Cook over medium heat, whisking occasionally, until the sugar and cocoa powder dissolve and the milk is steaming; do not boil.
Whisk in half of the chopped chocolate until melted, then whisk in the remaining chocolate until smooth. Remove from the heat and whisk in the vanilla. Pour into mugs and top with marshmallows or whipped cream.