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 the Thermomix bowl and melt on 60 degrees, Speed 2, 4 minutes (or until melted and smooth).
Add the plain flour, self-raising flour and add the vanilla extract, eggs and salt and mix on Speed 5, 5 seconds. Scrape down the sides of the bowl and repeat for a further 5 seconds (or until smooth and combined).
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, place the butter, brown sugar and milk into the Thermomix bowl. Melt on Speed 2, 60 degrees, 3 minutes (or until slightly thickened. Allow to cool slightly.
Sift the icing sugar mixture into the bowl and mix on Speed 5, 5 seconds. Scrape down the sides of the bowl and repeat for a further 5 seconds.
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.