01 - Preheat oven to 400°F. Line a baking sheet with parchment paper and set aside.
02 - In a mixing bowl, gently toss the sliced pears with granulated sugar, lemon juice, and ground cinnamon until evenly coated. Set aside to macerate.
03 - On a lightly floured surface, roll out the puff pastry sheet to smooth any seams. Cut into 6 equal rectangles.
04 - Arrange several pear slices in the center of each pastry rectangle, leaving a 1/2-inch border around the edges.
05 - Fold the edges of each pastry rectangle slightly over the pear filling to create a raised rim.
06 - Brush the exposed pastry edges generously with the beaten egg to ensure a glossy, golden finish after baking.
07 - Transfer the assembled pastries to the prepared baking sheet. Bake for 20 to 25 minutes until the pastry is puffed and golden brown and the pears are tender.
08 - While the pastries bake, combine the apricot jam and water in a small saucepan over low heat. Stir until the mixture becomes smooth and liquid. Strain through a fine mesh sieve if desired for a clearer glaze.
09 - Remove the pastries from the oven and, while still warm, brush the pear tops with the warm apricot glaze. Allow to cool slightly before serving. Best served warm or at room temperature.