Lay puff pastry on a lightly floured surface. Cut square in half to make two rectangles; save one for another use. With a floured rolling pin, roll out one rectangle to 7 by 14 inches. Transfer to a buttered 12- by 15-inch baking sheet.
Brush all but a 1-inch border of dough with the apricot jam. Lay two rows of overlapping pluot wedges over jam. Brush edges of dough with egg and fold, pinching corners to seal. Brush edges of tart with egg. Sprinkle fruit with sugar.
Bake in a 375° oven until pastry is browned and pluots are tender when pierced, 35 to 40 minutes. Let cool.