Arrange a rack in the center the oven and preheat to 425 degrees F.
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.
In a small saucepan, combine the preserves and brandy, bring to a boil, and cook, stirring, for 1 minute. While the tarts are still warm, brush them lightly with the apricot glaze.
Serve the tarts warm or at room temperature with ice cream or sweetened whipped cream.
Recipe courtesy Gourmet Magazine