In saucepan, melt butter. Stir in sugar. Cook until sugar dissolves and mixture caramelizes, stirring constantly. Add spices. Fold in ice cream. Stir until it dissolves. Refrigerate mix.
To assemble drink: Heat glass coffee mug. Stir in 3 tbsp mix plus 1 shot dark rum. Top with boiling water. Garnish with cinnamon stick.