Preheat the oven to fan 200C/ conventional 220C/gas 7. Melt the butter in a deep, heavy-based, 20cm frying pan (one that goes in the oven). Stir in the sugar and cook over a medium heat for about 5 minutes until the butter and sugar turn into a golden caramel. Take the caramel off the heat and leave to get cool, but not firm.
Meanwhile, unroll the puff pastry onto a floured surface and cut into a 24cm disc.
Halve the bananas lengthways. Arrange in the caramel, un-cut side down, fitting whole bananas snugly around the edge of pan, then filling in centre by cutting the bananas into smaller lengths if you need. Lay the pastry disc on top of the bananas and tuck the edges down the sides of the pan. Bake the tarte for 20-25 minutes in the oven until the pastry is golden brown. Leave to cool for about 5 minutes before turning out.
To turn the tarte out, put an upturned, large plate on top of the pastry. Spread your hand across the plate to get a good grip. Quickly flip the pan upside down and then carefully lift it off. The caramelised bananas should now be facing up. Serve slices of the tarte with vanilla ice cream or a good dollop of crème fraîche.