Wash the persimmon, use a knife to remove the stem, the leaf-like part on top and any seeds. Cut the fruit into wedges and then in pieces. Put them in a heavy-bottomed saucepan with the sugar, water, lime juice, vanilla pod and cardamom seeds. Bring to the boil, stirring from time to time, then put the lid on and leave over a low heat to simmer for 5 minutes, to reduce the liquid slightly. Turn the heat off, and remove the cardamom seeds and vanilla pod. Blend the rest to obtain a purée, filter it through a strainer and leave to cool. Now distribute the persimmon purée among the glasses, pour the sparkling wine in very slowly and... cheers!