Using a 9-inch (23 cm) flat-sided cake pan as a template, cut a circle out from the puff pastry. Using a fork, poke holes all over to provide ventilation. Set aside.
Peel and quarter the apples.
Preheat oven to 375°F (190°C).
In a large saucepan over medium heat, add butter and sugar and cook until light amber in color, stirring to help melt any lumps. Stir constantly until the color is a creamy light brown. Add the apples, stirring until they are coated in a thick layer of caramel.
Arrange the apple slices in concentric circles on the bottom of the cake pan. Press the apples tightly against each other, then pour the remaining caramel over the top.
Lay the circle of puff pastry on top. Tuck the puff pastry down the sides of the pan. (If pastry is already a circle and is larger than the pan, place over top, pinch excess around the edges like you would a pie, and tuck into the pan)
Bake for 45-50 minutes, until the pastry is golden brown and firm. Cool for about 1 hour, then invert onto a plate.