In a small pot, combine whipping cream, natural yogurt and brown sugar together. Bring to boil at medium heat and stir well till yogurt dissolved. Remove from heat and pass cream mixture through a fine sieve. Add vanilla extract, rum and stir well again.
Drop chocolate pieces into cream mixture and stir until smooth. Then lastly pour chocolate cream into small glasses and chill in the refrigerator for at least 2-3 hours or overnight.