Peel, core, and halve the apples. To prevent browning, place them in a bowl with water and lemon juice while preparing the caramel.
Set a 20 cm ovenproof frying pan or tarte tatin dish over medium heat. Melt the butter, then sprinkle the sugar evenly over it. Allow the sugar to melt and turn golden amber, swirling gently but not stirring. The caramel should have a rich aroma, not burnt.
Once the caramel is ready, remove from the heat. Arrange the apple halves in the pan, cut-side up, fitting them snugly together. They will shrink during baking, so pack them tightly.
Return the pan to medium to low heat and cook for 15 minutes, occasionally spooning caramel over the apples. They should soften slightly and take on a deep golden glaze. Sprinkle a pinch of cinnamon if using. Remove from heat and let cool for a few minutes.
On a lightly floured surface, roll out the puff pastry into a circle slightly larger than the pan. Trim the edges neatly. Prick the pastry all over with a fork to prevent puffing unevenly during baking.
Place the pastry over the apples, tucking the edges down the sides of the pan carefully using a spoon or spatula. This creates a neat seal and ensures the caramel doesn’t escape during baking.
Preheat the oven to 200°C (180°C fan). Bake the tart for 25–30 minutes, or until the pastry is golden brown and crisp. The caramel will bubble up around the edges.
Remove from the oven and let it stand for 5–10 minutes. This resting period allows the caramel to thicken slightly, which helps the apples stay in place when inverted.
Place a serving plate over the pan and, using oven gloves, swiftly but carefully flip the tart onto the plate. Lift the pan gently to reveal the glistening apples and golden pastry base.
Serve warm with a dollop of crème fraîche or vanilla ice cream. The tart is best eaten the same day when the pastry retains its delicate crispness.