Butter the brioche on both sides, then spread 4 tablespoons of the dulce de leche over 4 of the slices. Top each with another slice of bread. Cut into rough squares and arrange in a greased baking dish. Slice 1 of the bananas and scatter over the brioche.
Mash the remaining banana in a bowl, add the remaining ingredients and whisk together. Pour over the bread and leave to soak for 30 minutes.
Dot the remaining dulce de leche over the top of the pudding. Bake in a preheated oven, 160°C (325°F), Gas Mark 3, for 50–60 minutes until puffed and just cooked through.