Preheat the oven to 350°.
Line a large-rimmed baking sheet with parchment paper. Roll the puff pastry sheet into a 12-inch square on a lightly floured surface. Transfer to a baking sheet. Arrange pears in a single layer over pastry, leaving a 1-inch border.
Whisk the egg and 1 tablespoon of water in a small bowl until combined. Brush egg mixture over pastry.
Bake 15 minutes.
Stir together syrup, melted butter, and nutmeg in a small bowl. Remove pastry from oven and, reserving 2 tablespoons of the syrup mixture for later use, brush with syrup mixture.
Bake at 350° until deep golden brown, 15 to 20 minutes more.
Remove from the oven and brush with reserved 2 tablespoons syrup mixture. Cool slightly on pan, 5 to 10 minutes.
Sift confectioners’ sugar over the tart just before serving.