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Equipment: 1 x 20cm/8-inch round springform cake tin.
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Put the dried apricots into a small saucepan, cover them with the cold water, and drop in the cracked cardamom pods with their fragrant seeds. Put on the heat, then bring to the boil and let it bubble for 10 minutes - don't stray too far away from the pan, as by the end of the 10 minutes the pan will be just about out of water and you want to make sure it doesn't actually run dry as the apricots will absorb more water as they cool.
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Take the pan off the heat, place on a cold, heatproof surface and let the apricots cool. Preheat the oven to 180u00b0C/gas mark 4/350u00b0F. Grease the sides of your springform cake tin and line the bottom with baking parchment.
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Remove 5 of the dried apricots and tear each in half, then set aside for the time being. Discard the cardamom husks, leaving the seeds in the pan.
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Pour and scrape out the sticky contents of the pan into the bowl of a food processor. Add the almond meal, polenta, baking powder, superfine sugar and eggs, and give a good long blitz to combine.
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Open the top of the processor, scrape down the batter, add 2 teaspoons of lemon juice and the rosewater, and blitz again, then scrape into the prepared tin and smooth with a spatula. Arrange the apricot halves around the circumference of the tin.
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Bake for 40 minutes, though if the cake is browning up a lot before it's actually ready, you may want to cover loosely with foil at the 30-minute mark. When it's ready, the cake will be coming away from the edges of the tin, the top will feel firm, and a cake tester will come out with just one or two damp crumbs on it.
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Remove the cake to a wire rack. If you're using apricot jam to decorate, you may want to warm it a little first so that it's easier to spread; rose petal jam is so lusciously soft-set, it shouldn't need any help. Stir a teaspoon of lemon juice into the jam and brush over the top of the cake, then sprinkle with the chopped pistachios and leave the cake to cool in its tin before unspringing and removing to a plate.
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STORE NOTE: Store in an airtight container in a cool place for 5-7 days. In hot weather (or if the central heating's on) keep in fridge.
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FREEZE NOTE: The cake can be made ahead and frozen for up to 3 months (though the nuts may soften slightly on defrosting). Wrap the fully cooled cake (still on the springform tin base) tightly in a double layer of clingfilm and a layer of foil. To defrost, unwrap and leave it (still on the tin base) on a plate at room temperature for about 4 hours.
