In a saucepan, bring the milk and cream to a low boil. Remove from heat.

Whisk the cocoa powder and vanilla into the milk. Add the sugar and simmer over medium heat, stirring until the sugar is dissolved. Add the coffee liqueur and dark rum(or brandy) and stir well. Remove from heat.

Take 4 mugs, wet the rims and dip into cocoa powder. Pour hot chocolate into mugs and top with whipped cream and grated chocolate.