Preheat the oven to 425ºF. Line a baking sheet with parchment paper or a Silpat.
Slice the apples into thin (about 1/4-inch) pieces. Place them in a large bowl then add the lemon juice, vanilla extract and brown sugar to the bowl, tossing to thoroughly combine. Set aside.
Unfold the sheet of puff pastry onto the lined baking sheet. Lightly score the dough by cutting a border 1 inch from the edges (do not cut through the pastry). Prick the pastry all over with a fork. Shake off any excess liquid from each apple slice then arrange them on the puff pastry inside the border area.
Whisk together the egg with 1 Tablespoon water. Brush the edges of the pastry with the eggwash then bake the tart for 15 to 17 minutes until golden and puffed.
Remove the tart from the oven oven, drizzle it with caramel sauce and sprinkle it with sea salt. Slice and serve immediately.
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