In a large bowl, combine apples, sugar, melted butter, lemon juice, cinnamon, vanilla, and salt. Set aside for 15 minutes.
Over a lightly floured surface, roll puff pastry into a 14-inch circle. Transfer rolled-out dough onto a parchment paper lined baking sheet. Sprinkle 1 tablespoon of flour evenly over the pastry dough.
Use a slotted spoon to transfer the apples to the pastry dough, leaving a 2-inch border. Fold the edges of the dough over the apples in a free-form fashion, creating pleats as you go. Patch up any tears by pinching a bit of dough from the edge. Brush the folded edge of the pastry with the beaten egg. Sprinkle with coarse or turbinado sugar if desired. Chill the assembled tart in the fridge for 15 to 20 minutes (if time allows).
Pre-heat the oven to 350°F.
Bake the galette for 50-55 minutes, or until the apples are tender and the crust is golden and cooked through. Transfer the pan to a rack and let cool.
To make the salted caramel. Heat granulated sugar in a medium saucepan over medium heat, stirring constantly with a rubber spatula or wooden spoon. Sugar will form clumps and eventually melt into a thick brown, amber-colored liquid as you continue to stir. Be careful not to burn. Once the sugar is completely melted, immediately stir the butter into the caramel until it is completely melted, about 2 minutes. Slowly pour in the heavy cream while stirring. Since the heavy cream is colder than the caramel, the mixture will rapidly bubble when added. Allow the mixture to boil for 1 minute. It will rise in the pan as it boils. Carefully remove from the heat and stir in 1 teaspoon of salt. Allow to slightly cool down before serving.
Drizzle galette with salted caramel, and serve with vanilla ice cream. Enjoy!
