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To make the dough, place the flour, sugar, salt and yeast in the bowl of a stand mixer fitted with a dough hook and mix to combine.
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Add the mashed banana, melted butter and most of the coconut milk and mix to form a rough dough. Add the rest of the milk as needed to form a soft, slightly sticky dough.
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Knead with the stand mixer on a high speed for about 5-10 minutes, until the dough is smooth and stretchy. The dough should be a bit sticky, but if it seems too wet you can add a little extra flour. If you don't have a stand mixer it can be kneaded by hand on a lightly oiled surface but it is quite a messy job.
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Place the dough in an oiled bowl, cover and place in the fridge to rise overnight. (Or in a warm place until doubled in size - 1-2 hours.)
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For the filling, mix together the light brown sugar and the spices in a bowl and set aside.
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Punch down the risen dough and give it a brief 30 second knead to knock out any air bubbles.
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Roll the dough out on a floured surface to an approx 30x45 cm / 12x18 inch rectangle and spread the softened butter evenly over the surface.
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Scatter over the cinnamon chai spice sugar mixture and press it down gently.
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Roll the dough up tightly from one of the long edges into a sausage and trim off and discard the ends.
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Use a sharp knife to slice the roll into 9 even slices then arrange them cut side down in a 23cm/9inch square tin lined with baking parchment.
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Cover loosely and set aside to rise for 30-40 minutes until puffy. Meanwhile, preheat the oven to 180C/350F/gas mark 4.
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Once the buns have risen, bake for 30-40 minutes, until the internal temperature reaches 94C/201F on a probe thermometer. Cover them loosely with tin foil partway through baking if the tops start to colour too much.
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Leave to cool in the tin for 30 minutes then carefully lift them out using the baking parchment and place on a wire rack.
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To make the glaze, sift the icing sugar into a bowl and gradually stir in the milk and vanilla until it forms a thick but pourable glaze. Drizzle the glaze over the tops of the buns and serve.