Melt butter and chocolate in a medium heatproof bowl in 15-20 second increments in the microwave, stirring after each, until mixture is smooth. Remove from heat and whisk in brown sugar, cinnamon, and salt.
Bring 2 ½ cups water to a boil. Remove from heat and add rum. Whisk in chocolate-butter mixture.
Serve hot. Top with marshmallows, whipped cream, and nutmeg.