01 - Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper and set aside.
02 - In a mixing bowl, gently toss the pear slices with granulated sugar, lemon juice, and ground cinnamon until evenly coated. Set aside to macerate briefly.
03 - On a lightly floured work surface, roll out the puff pastry sheet to smooth any seams. Using a knife or pastry wheel, cut the sheet into 6 even rectangles.
04 - Arrange several pear slices in the center of each pastry rectangle, leaving about a 1/2-inch border around the edges. Fold the pastry edges inward slightly to create a rim around the filling.
05 - Lightly brush the exposed pastry edges with the beaten egg to ensure a deep golden, glossy finish after baking.
06 - Transfer the assembled pastries to the prepared baking sheet. Bake for 20 to 25 minutes, until the pastry is puffed and deeply golden and the pears are fork-tender.
07 - While the pastries bake, combine the apricot jam and water in a small saucepan over low heat. Stir until the mixture becomes fluid and smooth. Strain through a fine-mesh sieve if desired for a clearer glaze.
08 - Remove the pastries from the oven. While still warm, brush the pear tops generously with the apricot glaze. Allow to cool slightly before serving. Best enjoyed warm or at room temperature.