Preheat your oven to 180°C. Grease a 22cm loaf tin and line the base with some baking paper. Beat the eggs and castor sugar together for a minute or two, until pale and creamy. Add the melted butter, milk and vanilla extract. Mix to combine. Sift in the flour, baking powder and salt. Add the bran and cake mix. Mix until everything is just combined. Pour the mixture into your prepared tin. Bake for 45 minutes, or until a skewer inserted into the centre comes out clean. Allow to cool completely before removing and slicing.