How to Make It
In a heavy, medium saucepan, bring the sugar and water to a boil. Cook over moderate heat, without stirring, until a deep amber caramel forms, about 12 minutes. Remove the pan from the heat. Slowly and carefully add a little of the cream to stop the cooking, then whisk in the remaining cream until the sauce is smooth. Let cool to room temperature.
In a large saucepan, simmer the milk with the vanilla bean over moderately low heat for 5 minutes. Remove from the heat and stir in the coffee liqueur. Remove the vanilla bean and scrape the seeds into the milk. Using an immersion blender, beat the milk until a layer of froth forms. Pour off the milk into warm mugs, then spoon the froth on top and drizzle with the caramel sauce. Serve at once.