In a small saucepan, combine dried apricots, 250ml/1 cup of cold water, and cracked cardamom pods with their fragrant seeds. Bring to a boil and simmer for 10 minutes, keeping a close eye to prevent the pan from running dry as apricots absorb water as they cool.
After removing the pan from heat, allow the apricots to cool. Meanwhile, preheat your oven to 180°C/160°C Fan/gas mark 4/350ºF. Don't forget to grease the sides of your springform cake tin and line the bottom with baking parchment.
Begin by removing 5 dried apricots, tearing each in half, and setting them aside momentarily. Next, discard the cardamom husks, ensuring the seeds remain in the pan.
Transfer the sticky pan contents into a food processor. Add ground almonds, polenta, baking powder, caster sugar, and eggs. Give it a thorough blitz for perfect integration.
Uncover the processor, scrape the batter, add 2 tsp lemon juice and rosewater, blitz, then spread in the tin and arrange apricot halves around the edge.
Begin baking for 40 minutes. If the cake browns too quickly, consider loosely covering it with foil after 30 minutes. To check for doneness, look for the cake to pull away from the tin's edges, the top to feel firm, and a cake tester to reveal only one or two damp crumbs.
Place the cake on a wire rack. If using apricot jam for decoration, warm it briefly for easier spreading; rose petal jam usually spreads effortlessly. Add a teaspoon of lemon juice to the jam, brush it onto the cake's top, sprinkle with chopped pistachios, and let the cake cool in the tin before transferring it to a plate.