Preheat oven to 180°C bake. Line a 20cm x 30cm sheet pan or 20cm cake tin with baking paper.
In a large bowl, mash bananas then whisk in egg and melted butter. Stir through Banana Cake Mix.
Transfer to sheet pan or cake tin and bake for 30-40 minutes, until golden and cooked through.
To make brown butter icing, place butter in a medium pot on low-medium heat and cook for 10-12 minutes. It will foam, then settle and will have golden brown flecks through the butter. Transfer to a heatproof bowl and put in the fridge to cool and set.
Once butter has cooled and solidified to a soft consistency, use electric beaters to beat for about 4 minutes, until pale and smooth. Add icing sugar and milk (a little at a time) and continue to beat for another 5 minutes, until fluffy.
Once cake has cooled completely, ice with brown butter icing and serve.