Preheat the oven to 400 degrees.
Unfold the sheet of puff pastry onto a cutting board and cut off one portion, so you're left with 2/3 of the pastry sheet.
Place a sheet of parchment paper on a cookie sheet, and move the puff pastry onto it. Score the edges of the puff pastry, roughly every 1", to ensure a fluffy edge that will rise above the pear filling.
Whisk together the butter, brown sugar, grated ginger, vanilla extract, cinnamon, and nutmeg in a small bowl. Brush this over the puff pastry, leaving a small, approximately 1" frame around the edge of the dough.
Cut the pears into quarters, removing seeds, and cut thin, approximately 1/4" slices to arrange on top of the pastry dough.
Bake for about 20 minutes, until dough is golden and pears are tender.