Heat milk and vanilla in a heavy saucepan over medium heat, stirring often (do not boil). Remove from heat. Place white chocolate in a medium bowl. Gradually whisk about one-fourth of hot mixture into chocolate, whisking until chocolate melts; add to remaining hot mixture, whisking constantly. Stir in brandy and creme de cacao. Garnish, if desired, with whipped cream and/or grated white chocolate.
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