Preheat the oven: Preheat your oven to 375°F (190°C).

1. Prepare the apples: Peel, core, and slice the apples into quarters or wedges.
2. Make the caramel: In a 9-inch (or 10-inch) oven-safe skillet, melt the butter over medium heat. Once melted, add the granulated sugar and brown sugar. Stir occasionally until the sugars dissolve and the mixture turns into a golden caramel, about 5-7 minutes. Add the vanilla extract, cinnamon, salt, and lemon juice to the caramel, stirring to combine.
3. Arrange the apples: Arrange the apple wedges in the caramel, placing them closely together and layering them slightly. Cook the apples in the caramel for 10-15 minutes, occasionally stirring to coat the apples in the syrup. The apples should soften slightly.
4. Prepare the puff pastry: Roll out the puff pastry on a lightly floured surface and cut it to the size of your skillet, making sure it will fully cover the apples.
5. Assemble the tart: Carefully place the puff pastry on top of the apples in the skillet, tucking the edges in around the apples. Use a fork to poke a few holes in the center of the pastry to allow steam to escape while baking.
6. Bake the tart: Transfer the skillet to the preheated oven and bake for 25-30 minutes, or until the pastry is golden brown and puffed.
7. Flip the tart: Remove from the oven and let it cool for a few minutes. Carefully flip the tart onto a serving plate. Be cautious as the caramel will be hot!
8. Serve: Serve warm, optionally with a scoop of vanilla ice cream or a dollop of whipped cream.