Pre-heat the oven to 170°C (338℉) and line/grease a 7" (18cm) springform pan.
Add the butter, chocolate, sugar and milk to a pan and heat until the chocolate and butter is almost melted (it will continue to melt even off the heat).
Put to one side to cool for a short while.
Add the egg, vanilla and white chocolate/butter mixture to a bowl and whisk everything together.
In another bowl, add the flour. From this, remove a couple of tablespoons of flour and place it in another bowl.
Throw in the blueberries into the bowl with only a couple of tablespoons of flour, and stir until they are well coated.
Add the baking powder to the remaining flour and give them a good mix. You could sift them together, if you like.
Add the flour mixture to the wet ingredients, and gently fold in.
Add the remaining flour/blueberry mixture and mix gently until pretty much combined (it's okay to have some flour still not incorporated).
Pour into the prepared pan and bake (in the lower part of the oven) for around 40-45 minutes.
Start checking at the 40 minute mark, and if the cake is browning a bit too much, cover it with some foil.
The cake is ready when an inserted skewer comes out clean.
When ready, remove from the oven.
Allow to cool in the pan for around 10 minutes, then remove the edges of the springform.
Leave on a wire rack until it is completely cold.