Peel and core the apples, then cut each in half from top to bottom.
Place the sugar into an ovenproof 190mm frying pan with the cold water. Place the pan over a medium heat and stir to a boil. Once boiling, remove the spoon and stop stirring. Increase the heat and continue cooking to a deep brown caramel.
Remove the pan from the heat and swirl in the butter, followed by the Calvados.
Allow the caramel to cool slightly, then pack the apples halves into the pan tightly, with the outside curve of the apples following the curve of the pan (try and keep the finished appearance in mind when assembling).
Cover with foil and place in the oven at 200C/Gas 6 for approx. 30 mins. Remove the foil and continue cooking until the apples are tender.
Remove the pan from the oven and allow to cool a little. Then, using your hand, press the apples very gently into the shape of the pan.
Carefully pour off the liquid into a small saucepan, bring to a boil and reduce slightly until thick and syrupy. Spoon the syrup over the apples, retaining a little for later, then place in the fridge to chill.
Cut the puff pastry into a disc slightly larger than the pan. Lay the pastry over the apples, drawing in and crimping the edges. Place into the oven at 200C/Gas 6 and bake 20 mins.
Remove the tart from the oven, place a plate on top, and invert the tart. Brush with the remaining syrup.
Cut into portions with a sharp serrated knife and serve warm or cold with sweetened whipped cream, crème frâiche or vanilla ice cream.
Recipe by appetite magazine at https://www.appetitemag.co.uk/tarte-tatin-2/