Cut apple halves crosswise into 1/16-inch-thick slices.
Roll out pastry sheet on a lightly floured surface into a 12 1/2-inch square and cut out 4 (6-inch) rounds. Transfer the rounds to a lightly buttered baking sheet and arrange the apple slices in overlapping concentric circles on them. Sprinkle each round with about 1 tablespoon of the sugar and dot each with 1 tablespoon of the butter.
Bake until golden brown, about 30 minutes.