In a large saucepan slowly add masa harina to the warm water, whisking until combined. Add coconut milk, chocolate, cream of coconut, and ground anise. Whisk over medium heat just until boiling; reduce heat. Simmer, uncovered, about 10 minutes or until chocolate is completely melted, whisking occasionally.
Meanwhile, in a small chilled bowl combine whipping cream and powdered sugar. Beat with an electric mixer on medium-high speed until soft peaks begin to form. If desired, gradually beat in the rum. Beat until soft peaks form (tips curl). Serve immediately on top of the champurrado. If desired, garnish with shaved fresh coconut.