In a saucepan, bring the milk and cream to a low boil. Remove from the heat.
Whisk the cocoa and vanilla into the milk. Add the sugar and simmer over medium heat, stirring, until the sugar is dissolved. Add the coffee liqueur and rum and stir well.
Remove from the heat and pour into 4 mugs. Top with a spoonful of whipped cream and grated chocolate. Serve.
Yield: 4 servings