Preheat the oven to 180C/350F/Gas 4.
Melt the caster sugar and butter together in a small ovenproof frying pan over a medium heat. Add the plums and cook until caramelised - about five minutes.
Whisk together the flour, soft brown sugar, eggs and milk and then pour this mixture over the caramelised plums.
Put the frying pan in the preheated oven and cook the pudding for ten minutes, or until the top is golden-brown.
Remove the pudding from the oven and carefully turn out onto a serving plate.
To serve, spoon a dollop of yoghurt onto the pudding and dust with icing sugar.