In a small saucepan, combine dried apricots, cardamom pods with fragrant seeds, and cold water. Heat, bringing it to a boil. Maintain a watchful eye for 10 minutes to prevent the pan from running dry, as apricots absorb more water as they cool.
After removing the pan from the heat, allow the apricots to cool. Then, preheat your oven to 180 degrees Celsius (or 350 degrees Fahrenheit) while you prepare your springform cake tin. Grease its sides and line the bottom with baking parchment.
Start by removing 5 dried apricots, tearing each one in half, and setting them aside. Next, discard the cardamom husks, ensuring you leave the seeds in the pan.
Transfer the sticky pan contents into a food processor. Then, add almond meal, polenta, baking powder, superfine sugar, and eggs. Finally, give it a thorough blend for perfect consistency.
Open the processor, scrape the batter, add 2 tsp lemon juice and rosewater, blitz again, and spread into the tin. Arrange apricot halves around the edge.
Bake for 40 minutes, and if the cake is browning too quickly at the 30-minute mark, consider loosely covering it with foil. You'll know it's ready when the cake pulls away from the tin edges, the top is firm, and a tester comes out with only a few crumbs.
Move the cake to a wire rack. If you plan to use apricot jam for decorating, consider warming it for smoother spreading. Rose petal jam, being naturally soft-set, typically doesn't require heating. Blend a teaspoon of lemon juice into the jam, generously brush it over the cake's surface, sprinkle with chopped pistachios, and allow the cake to cool in the tin before safely removing it onto a plate.