Pre-heat oven to 150c
Using a heavy kitchen knife, bash the lemongrass all over without cutting it.
Place the rice in a lightly greased ovenproof dish, cover with the coconut milk, full fat milk, add the sugar, vanilla and lemongrass and mix to combine.
Cover dish with 2 layers of foil, place in the oven to cook for 1 ½ -2 hours or until the rice is tender.
While the rice is cooking prepare the bananas by peeling them and cutting each into 2.5 cm slices diagonally.
Heat a non-stick frying pan, add the butter and banana slices and fry gently for 2-3 minutes until then are lightly coloured, then add the sugar and cook together until the sugar caramelises and the bananas are beautifully golden and caramelised. Season the bananas lightly with a sprinkling of sea salt. Finely grate the lime over the bananas.
To Serve, remove the cooked baked rice pudding from the oven, remove the lemongrass, top with the caramelised bananas and serve.