Preheat oven to 150 degrees celsius (fan-forced). Grease and line a 20cm round cake tin with baking paper (on the base and sides) and set aside.
Place the butter, brown sugar, milk and white chocolate melts into a microwave-safe bowl and heat on 50% power in 30 second bursts until melted (stir every 30 seconds). Allow to cool slightly. (see notes).
Sift over the plain flour, self-raising flour and add the vanilla extract, eggs and salt. Mix together until smooth.
Pour the mixture into the prepared cake tin. Cover with foil and bake for 60 minutes or until a skewer inserted into the middle comes out with just a few crumbs on it. Allow the cake to cool before transferring to a wire rack or plate.
To make the caramel frosting, melt the butter in a microwave-safe bowl on 50% power.
Add the brown sugar and milk and stir together. Place back into the microwave for 2-3 30 second bursts or until slightly thickened. Allow to cool slightly for a few minutes.
Sift the icing sugar mixture over the top of the mixture and mix together with a whisk.
Spread the caramel frosting over the top of the caramel mud cake and serve.
Store in an airtight container at room temperature for up to 1 week.
You can use a saucepan over a cooktop instead of the microwave if you prefer.