First, preheat your oven to 200°C (400°F). This helps get the puff pastry nice and golden.
Grease an ovenproof frying pan or tart tin with a little salted butter. This will prevent sticking and add flavor.
Pour the sugar and water into the pan and gently heat on medium. Stir just a little until the sugar dissolves. Then let it bubble without stirring, until it turns a rich golden caramel color. Keep an eye on it because caramel can burn fast.
Once your caramel is ready, carefully add the apple pieces into the pan, arranging them neatly. The caramel will bubble up, so be cautious.
Cook the apples in the caramel for about 10 minutes on medium heat. This softens the apples and lets them soak up the caramel flavor.
While the apples cook, roll out your puff pastry on a floured surface to fit just over the pan. It should be about ⅛ inch thick.
Carefully place the pastry over the apples in the pan. Tuck the edges down around the apples to seal them in.
Transfer the pan to the oven and bake for 25-30 minutes until the pastry is puffed and golden brown.
Remove from the oven and let it cool for 5 minutes. Then place a large plate on top of the pan and quickly but carefully flip the tart over so the apples are on top.
Serve your tarte tatin warm with a dollop of whipped cream or crème fraîche.