Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
In a small bowl, beat the egg with the water.
On a lightly floured surface, roll out the puff pastry to a large rectangle, about 14 by 8 inches. With a small, sharp knife, lightly score the outer 3/4-inch edge of each side. Using your finger or a pastry brush, brush this outer edge with the egg wash. Fold the outer edge over onto the dough to make a border, pressing gently to adhere, and paint the top lightly with the egg wash. With a fork, score the inner base of the tart. Place on a prepared baking sheet and refrigerate for 20 minutes.
Bake the pastry shell until light golden brown and crisp, about 20 minutes. Cool completely on a wire rack.
In a small bowl, beat the cream to soft peaks.
In a medium bowl, beat together the mascarpone, sugar, orange juice, and orange zest until smooth. Fold in the whipped cream.
Spread the cream mixture evenly over the bottom of the tart shell. Arrange the berries decoratively over the top.
In a small bowl, whisk the jam and apple juice until the jam is smooth and a spreadable consistency. Using a pastry brush, lightly glaze the top of the berries with the jam.
Slice the tart into 8 portions. Spoon puddles of the melted ice cream into the center of 8 dessert plates and top with slices of the tart. Garnish with mint sprigs and serve.