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Prepare to the end of step 4 a few hours before baking. If the sauce overthickens, reheat gently until runny, then pour over the pud.
Preheat the oven to 180°C, fan 160°C, gas 4. Toast the pecans on a baking sheet for 6-8 minutes, then roughly chop and cool. Grease a deep 2-litre ovenproof baking dish, about 20 x 28cm base measurement, with butter.
In a saucepan, mix all the sauce ingredients with 225ml water and a pinch of salt over a low heat. Once the sugar has dissolved, remove from the heat. It will be very thin, but will thicken as it bakes with the pudding.
Mash 2½ bananas in a bowl, then add the eggs, milk, melted butter and vanilla, followed by the sugar, and mix well.
Tip the wet ingredients into the dry and whisk until fairly smooth. Pour into the prepared baking dish and top with a few more pecans and the remaining banana, sliced.
Slowly pour the sauce all over the pudding, then bake on a tray for 35-40 minutes. It should be risen, golden brown and firm in the centre. Leave to stand for 10 minutes and serve with ice cream or pouring cream, scattered with the rest of the nuts.