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Combine milk, vanilla, cayenne pepper, chocolate and sugar in a saucepan. Cook and stir until chocolate melts.
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If you prefer thicker hot chocolate, combine cornstarch and 1-2 Tbsp cold water, pour into milk mixture and cook, stirring constantly, for 1 to 2 minutes or until mixture thickens.
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Pour into cups and garnish with the cinnamon stick. Serve immediately.