Place the butter into a small saucepan and place over a medium heat. Cook, stirring every now and then, until the butter has foamed and turned a light brown colour. (Keep watch, as it can easily burn.) Pour into a bowl to cool a little – the butter should now weigh 82g.
In a large bowl add the egg, egg yolk and sugar and using an electric whisk, whisk for around 6-7 minutes until the mixture is very pale and thick.
Mix together the flour and baking powder, and sift into the egg/sugar mixture. Very gently fold in. Then add the sourdough starter and again mix in very gently.
Take a large spoonful of the batter and mix it into the browned butter. Then pour the butter mixture back into the batter and mix in carefully but thoroughly. Place clingfilm directly onto the batter, to stop a skin forming, and place into the fridge for 3 hours.
With an hour to go on the batter, liberally butter and flour your baking tin. Then place in the freezer to chill.
Preheat the oven to 220C/200 Fan with about 30 minutes to go. Then spoon batter into each madeline shell about 2/3 full, and bake for 8-9 minutes. As soon as they are out of the oven, tap them out onto a wire rack and leave to cool.
After the madelines have cooled for about 10 minutes, melt the dark chocolate in a microwave in 30 second burst, stirring between each. Then dip each madeline in the melted chocolate and leave to set on baking paper.