Pre-heat the oven to 175°C and line/grease a 6" (18cm) springform pan.
Add the butter, chocolate, sugar and milk to a pan and heat until the chocolate and butter have just melted and the sugar has dissolved. Put to one side to cool for a short while.
Add the egg and vanilla and mix just until combined. Add the flour and baking powder and stir until everything is combined (don't over mix).
Pour into the prepared pan and bake for around 40-45 minutes until an inserted skewer comes out clean. Allow to cool for around 10 minutes, then remove the pan and allow to cool on a wire rack until it is completely cold.