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Whizz the biscuits to crumbs in a food processor or put in a strong plastic bag and bash with a rolling pin. Add the butter and whizz again briefly, then tip the buttery crumbs into a 22cm fluted tart tin. Use the back of a spoon to press the crumbs into the tin and up the sides until the whole case is lined. Chill for at least 10 mins.
Heat oven to 200C/180C fan/gas 8. Halve the bananas lengthways and tip into a shallow roasting tray or baking dish. Squeeze over the lime juice, scatter with the brown sugar and bake in the oven for 15-20 mins until caramelised. Leave to cool slightly, then thoroughly mash and spread evenly over the tart base.
Tip the caramel into a saucepan, bring to a simmer and bubble for a few minutes to thicken. Add a pinch of flaky sea salt. Crush the banana chips using a rolling pin on a chopping board. Take the pan off the heat and stir in most of the banana chips, then spread the mixture over the banana layer and put back in the fridge for at least 4 hrs to set.
To make the peanut butter cream, beat the peanut butter with the icing sugar and 140ml of the cream until smooth. Whisk the rest of the cream until it just holds its shape, then fold through the peanut butter cream to ripple. Top the tart with pillows of the whipped cream. Scatter with the rest of the crushed banana chips and serve.