Place the persimmon in a pan along with all the other ingredients up to and including the cinnamon stick, bring to the boil, cover and simmer for approx. 5 mins., reduce a little. Remove the vanilla, cardamom and cinnamon, set aside. Puree the rest until smooth, press through a sieve if necessary, leave to cool.
Pour the persimmon puree into glasses, top up with the Prosecco and garnish with the vanilla pods.