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.
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