Preheat the oven to 400 degrees F.
In a large skillet over medium heat, add the butter, brown sugar and pumpkin pie spice. When it is melted, add the pears. Cook until the pears are slightly softened and the liquid thickens, about 5 to 6 minutes. Let cool.
On a floured surface or on parchment paper, roll out the chilled dough into a 12-inch-by-10-inch rectangle. Spread the cooled pear mixture in the middle of the rectangle, fold in the short ends, and roll the crust over enclosing the pear mixture. Place the strudel, seam side down, onto a baking sheet.
In a small bowl beat the egg with a tablespoon of water. In another small bowl mix together the remaining 1/2 teaspoon pumpkin pie spice and sugar. Brush the strudel with the egg wash and sprinkle with half the spiced sugar. Make five small slits on top to let the steam escape. Bake until golden brown, about 25 to 30 minutes. Let cool for 30 minutes.