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Pit the plums. Cut into pieces and puree in a food processor.
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Transfer to a saucepan. Add 1/4 cup of sugar, cinnamon, and cardamom.
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Cook until the sugar has dissolved. Set aside.
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Beat the remaining 1/2 cup of sugar and the egg yolks until creamy.
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Whisk the milk, cream, vanilla, and 1/4 cup of the remaining sugar in a saucepan over medium heat until the sugar has dissolved.
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Slowly pour a small amount of the warm mixture into the egg yolk mixture, whisking constantly to temper the eggs.
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Combine the egg and creamy mixtures.
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Whisk in the cooked plums and the cinnamon.
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Reheat, whisking constantly until the mixture thickens. It should coat the back of a wooden spoon.
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Pour into a bowl. Cover with plastic cling film, making sure the plastic touches the top of the mixture.
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Refrigerate for 4 hours or overnight.