In a saucepan, heat the sugar over high heat. To prevent burning, gently shake the pan but do not use any utensils. Remove from heat, add the butter, and stir vigorously.

Cut the apples into quarters, remove the seeds, and peel them. Cut each quarter in half. Arrange the apple pieces tightly over the caramel.

Cover with the puff pastry. Bake at 400°F (200°C) for about 30 minutes.

Let cool slightly, then invert the tart onto a plate.