Preheat oven to 375 °F and grease a 6-inch round cast iron pan (not a ceramic dish or glass pie plate)
Bring water, sugar, and lemon juice (or white corn syrup) up to a boil without stirring. Boil sugar, occasionally brushing the sides of the pot, until it is a light amber colour, about 5 minutes. Pour caramelized sugar into bottom of prepared pan, and place apples in pan (they should fit snuggly). Bake apples for 25 –30 minutes, until bottom of apples are golden and caramelized. Remove pan from oven, and carefully flip apples over, so that the caramelized half is now facing up. Cut a disk of puff pastry about a half inch larger in diameter as the pan and dock pastry with a fork. Place pastry over apples, tucking the ends of the pastry into the pan. Return pan to oven and bake for about 25 minutes, until pastry is golden.
Let tart cool 20-30 minutes, then, carefully turn tart out onto a plate to serve.
For the Salted Caramel Sauce:
Bring water, sugar and corn syrup up to a boil in a heavy-bottomed saucepan. Boil without stirring, brushing the sides of the pan occasionally with a brush dipped in water. Cook for about 10 minutes, until sugar turns an amber colour. Remove from heat and whisk in cream, taking care as it will steam, then stir in 1 tsp fleur de sel. Allow to cool, then chill until ready to serve.
Sauce can be warmed to serve, then sprinkled with remaining ½ tsp fleur de sel as garnish