Preheat the oven to 180ºC/350ºF/gas 4.
Place 50g of the butter in a non-stick 20cm ovenproof frying pan and melt over a medium heat. Add 100g of the sugar and a tablespoon of water and cook for 5 minutes. Bring to the boil for a further 5 minutes until you get a nice buttery caramel. Be careful though, the caramel gets very hot! Toss in the plums and shake around to coat them with the caramel. Remove the pan from the heat.
In a large bowl, beat the remaining butter and sugar together with a wooden spoon until light and fluffy. Add the egg yolks one at a time, beating each one in well before adding the next. Gently fold in the flour, polenta and cocoa.
In a small, clean, dry bowl, beat the egg whites until they form stiff peaks. Fold through the cake mix with a large metal spoon. Spoon the mixture over the caramelly plums in the pan and smooth out. Pop the pieces of chocolate into the batter.
Put the pan in the oven and bake the cake for about 40 minutes. While the cake is cooking, if serving with ice cream, line a shallow tray with greaseproof paper and sprinkle with the coconut. Take 6 scoops of vanilla ice cream and roll them in the coconut. Put them on the tray and stick them back in the freezer.
To test whether your cake is done, insert a wooden skewer into the centre – it should come out clean. If not, pop the cake back in the oven for a little longer. Turn out the cake on to a plate and leave to cool a little. Serve the warm cake with a scoop of ice cream, if using, on the side.