Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.

Let the frozen puff pastry sheet thaw at room temperature for 15 to 20 minutes until pliable but still cold.

Peel, core, and slice the apples into 1/4-inch-thick even slices.

Melt the butter in a medium skillet over medium heat, then add the sliced apples, brown sugar, cinnamon, vanilla extract, and salt. Cook for 4 to 5 minutes, stirring occasionally, until the apples soften slightly and begin to caramelize.

Meanwhile, whisk the egg yolk and water in a small bowl to make the egg wash.

Unfold the thawed puff pastry onto the prepared baking sheet. Brush the edges of the pastry with the egg wash, taking care not to let it drip over the sides.

Use a slotted spoon to transfer the cooked apples onto the pastry, leaving a 1/2-inch border around the edges. Arrange the apple slices in overlapping rows, then sprinkle with coarse sugar if desired.

Bake for 15 to 18 minutes at 400°F (200°C), until the pastry is puffed and deep golden brown. If the edges brown too quickly, tent loosely with foil. Allow to cool slightly before serving.