Heat oven to gas 4, 180°C, 160°C. Crush the cardamom pods then remove and crush the seeds (discard the husks), placing them in a mixing bowl.
Add the semolina, flour, baking powder and 125g (4oz) caster sugar and mix well. Beat the yogurt, eggs and vanilla essence together, add to the semolina and flour and blend until smooth. Place in a 23cm (9in) cake tin and bake for 30 minutes.
Simmer and reduce the pomegranate juice by half. Add remaining sugar and mix to dissolve — then cool.
Remove all the seeds from the pomegranate, add to the syrup and mix. Spoon over the cooked cake and serve.
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