Put the chestnuts into a blender and process until you get crumbs. Transfer this into a mixing bowl.
Puree the bananas in the blender, add the oil and vanilla. Pulse for a few seconds, then spoon this mixture into the mixing bowl. Add the other ingredients and mix well until sticky and dough-like.
Line a bread tin with baking paper and spoon in the mixture. Bake in the middle of the oven for about 45-55 minutes until golden on the outside and an inserted skewer comes out clean.
Cool on a wire rack, then decorate with sliced bananas, dipped in icing, or dust with icing sugar.