1. Preheat oven to 160C fan forced, line the sides and base of a 23cm tin.
2. Mix sugar and ground cardamom together, sprinkle on the base of the cake tin, place the plum halves cut side down in a circle on top of the sugar until the base is covered.
3. Place butter and sugar in a bowl and mix with an electric beater until pale. Add the eggs beating in one at a time, mix in zest and vanilla. Fold through almond meal, polenta and baking powder until combined. Spoon batter over the plums evenly and cook for 1 hour.