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Place the pudding rice, milk, vanilla and sugar in a saucepan and bring to a gently simmer. Leave to simmer, stirring regularly, for 15-20 minutes until rice is soft and tender to the touch and the milk has reduced a little. Don't worry if it is still quite runny it will thicken more as it cools.
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Cut the plums into quarters and remove the stones. Place into a saucepan and add the water, spices and sugar.
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Place the plums on a medium heat and simmer, stirring occasionally for 5 minutes then remove the star anise and cinnamon stick.
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Leave the plums on the heat for another 3-4 minutes until plums are soft but still just about holding their shape and the liquid is nicely coloured.
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If the juice isn't very thick, mix the cornflour with a drop of water and stir into the juice, if it is thick enough you can skip the cornflour.
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Serve the rice pudding topped with the plums, serve either hot or cold.