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Preheat your oven to 180 degrees Celsius (350 degrees Fahrenheit). Line a loaf pan with baking paper and set aside.
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In a microwave safe bowl, combine the butter and peanut butter, and microwave to melt completely. Stir to incorporate.
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In a large bowl, combine the mashed banana and peanut butter mixture with a wooden spoon. Add the caster and brown sugar, beaten egg and vanilla to this, stirring to incorporate all the ingredients.
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Add the flour, bicarb of soda and salt to the mixture, and stir until just combine. Be careful not to overbeat the batter.
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Pour into the prepared loaf pan, ensuring that it is evenly spread. Bake for 1 hour, or until a cake skewer inserted into the middle comes out clean. Allow to cool slightly, remove from the pan, and cut into even slices. Best served still warm.