Peel and halve the pears, then scoop out the cores using a melon baller. Lay the pears out on a tray lined with kitchen paper and pat them with more kitchen paper. Leave to dry uncovered for a few hours, or chill overnight if possible – it won’t matter if they discolour because they will be coated in caramel.
Roll out the puff pastry thinly on a lightly floured surface and cut out a 24cm round, using a similar-sized plate as a guide. Lift onto a baking sheet and chill while you prepare the filling.
Cut the butter into thin slices and scatter over the bottom of a 20cm, shallow, ovenproof pan. Sprinkle over the sugar. Arrange the pear halves neatly around the pan with one in the middle. Place over a medium heat until the butter and sugar have melted and formed a light caramel. Carefully shake the pan every now and again to ensure that the pears are well coated with the caramel and are evenly brown. Leave to cool slightly.
When ready to cook, preheat the oven to 200ºC/425ºF/gas mark 7. Drape the pastry over the pears and carefully tuck the edges down the side of the pan. Place the pan into the hot oven and bake for 15 minutes. Lower the oven setting to 180ºC/400ºF/gas mark 6 and bake for a further 10–15 minutes until the pastry is golden brown and crisp. Leave to cool.
To serve, dust the vanilla pods heavily with icing sugar, shaking off the excess. Turn out the tart tatin onto a serving plate, top with the sugar-dusted vanilla pods and serve with scoops of vanilla ice cream in small bowls on the side
