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

2. Prepare the Apples:

   • Peel, core, and quarter the apples.
   • If desired, sprinkle the apple quarters with cinnamon and a pinch of salt to enhance the flavor.

3. Make the Caramel:

   • In a heavy, oven-proof skillet (preferably cast iron), melt the butter over medium heat.
   • Once melted, add the sugar and cook until the mixture turns a golden amber color, stirring occasionally. This should take about 5-7 minutes.

4. Add the Apples:

   • Carefully add the apple quarters to the skillet, arranging them in a circular pattern. They should be packed tightly as they will shrink during cooking.
   • Cook the apples in the caramel for about 10 minutes, turning them gently to coat and soften slightly.

5. Add Vanilla:

   • Drizzle the vanilla extract over the apples and stir gently to incorporate.

6. Top with Pastry:

   • Roll out the puff pastry on a floured surface to fit the skillet. Place the pastry over the apples, tucking the edges down into the skillet around the apples.

7. Bake:

   • Transfer the skillet to the preheated oven and bake for about 25 minutes, or until the pastry is golden brown and puffed.

8. Cool and Invert:

   • Once baked, remove the skillet from the oven and let it cool for about 10 minutes.
   • To serve, place a large plate over the skillet and carefully invert the tart onto the plate. Be cautious of hot caramel that may spill out.

9. Serve:

   • Tarte Tatin can be served warm or at room temperature. It pairs beautifully with a dollop of whipped cream or a scoop of vanilla ice cream.

Tips:

• For a deeper flavor, you can mix in a splash of apple brandy or Calvados with the caramel.
• Experiment with different fruits like pears for a variation on this classic recipe!