Make the gingerbread spice mix: Combine the cinnamon, ginger, nutmeg and cloves in a small bowl, whisking to combine. Set aside.
Make the hot chocolate: Combine 1 cup of the milk and the brown sugar in a large heatproof bowl set over a pot of simmering water. Heat the milk mixture until steaming, whisking occasionally.
Add the chocolate to the hot milk and whisk to combine, continuing to heat it over the simmering water. Whisk the mixture for an additional 3 minutes, until shiny and emulsified.
Add the molasses and the gingerbread spice mix to the bowl, and whisk to combine.
Whisk in the remaining milk, adding it in a slow stream. Continue heating the hot chocolate until steaming, about 10 minutes, whisking occasionally.
Remove the bowl from the pot of water and pour the hot chocolate into mugs. Serve immediately, topped with marshmallows, if you'd like.