Note: If you prefer to not make your own caramel, skip to the next step of making the brownies. You can add ½ cup chopped candied or regular nuts into the batter instead.
Make the caramelized nuts: In a medium heavy-bottomed saucepan heat sugar and water over medium heat. Let the mixture bubble away until the sugar turns into reddish, golden caramel and reaches 250F/120C. Swirl and shake the pan occasionally (but not too much as this encourages clumping) to cook evenly and prevent the caramel at the edges from burning. Stir in the nuts, and immediately spread onto a tray lined with parchment paper. Allow to cool, then chop finely.
Make the blondies: Line the base and sides of an 8-inch/20cm square pan with foil and preheat the oven to 375F/190C. In a medium heat-proof bowl, place white chocolate and butter. Place the bowl over a saucepan of simmering water and stir occasionally until chocolate and butter have melted. Transfer mixture to a large bowl. Add sugar and mix to combine. Add egg, bananas, and vanilla and mix until smooth. Sift flour and baking powder, then fold just until combined. Fold in chopped nuts. Spoon into pan and bake for 30-35 minutes, until wobbly-set and golden on top. Allow to cool completely before slicing.