WHIPPED CREAM: In the mixing bowl stir to combine the whipping cream, vanilla extract, sugar, and cocoa powder. Cover and place the mixing bowl and the wire whisk in the refrigerator for at least 1 hour to give the chocolate time to dissolve. Remove and beat with chilled wire whisk at least 2 minutes, until you have stiff peaks.
COCKTAIL: Stir together the prepared hot chocolate, brandy, crème de menthe, and dark rum in the heatproof mug. Top with dollops of chocolate whipped cream and crushed Peppermint Altoids.