Preheat the oven to 200°C.
Gently heat the caster sugar in a 20cm non-stick ovenproof frying pan until it turns to caramel.
Add 1.5 tablespoons of water and the rum once the sugar has dissolved.
Remove the golden-brown caramel from the heat and stir in the butter.
Arrange the banana chunks tightly in the caramel without leaving gaps.
Roll out the puff pastry on a floured surface and place it over the bananas.
Tuck the excess pastry down the sides and brush with egg wash.
Bake in the oven for 20 minutes until the pastry is crisp and golden.
Drain any excess liquid and invert the tart onto a serving plate.