Preheat the oven to gas 6, 200°C , fan 180°C. Heat the butter and sugar over a medium-high heat in a Tatin pan or a 20cm ovenproof frying pan. Swirl the pan to combine the butter and sugar and continue cooking until you reach a toffee coloured caramel.
Turn the heat down and add the apple halves to the pan, tucking them tightly in around the perimeter and then filling the centre. Continue cooking on a lower heat for 8-10 minutes, while you roll the pastry out on a lightly floured surface to 1cm in thickness.
Prick a few times with a fork. Cut a round of pastry that is slightly larger than the diameter of the pan you are using.
Remove the pan from the heat and carefully drape the pastry over the pan, tucking the overhanging pastry in around the edges to secure it. Transfer the pan to the oven and bake for 20-25 minutes until the pastry is risen and golden brown in colour.
Remove from the oven and let the tart sit for 10 minutes before running a sharp knife around the edge to loosen it a little. Place a large plate on top of the pastry and invert quickly and carefully to release the tart onto the plate; the pan will be hot so use oven gloves. Transfer the tart to a wire rack and serve.
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