Peel, halve, core, and slice the pears lengthwise into paper-thin slices. Transfer to a large bowl and toss with the lemon juice to prevent browning. Toss with the granulated sugar and flour and set aside.
Preheat the oven to 350 degrees F.
Roll out the chilled dough on a lightly floured work surface into a 20by 15-inch rectangle about 1/4 inch thick. Carefully roll the dough around the rolling pin to make it easy to lift and unroll it over a 12 by 18-inch rimmed baking sheet (if the dough tears slightly, that's okay; just press it back together). Press the dough in to the bottom and up the sides of the pan, pressing any cracks together (it's a very forgiving dough). Trim off any dough hanging over the sides of the pan. Sprinkle the ground gingersnap cookies evenly over the dough and layer the pears horizontally over the gingersnap crumbs. Bake until the crust is golden brown and pulls away from the sides of the pan and the pears are tender, about 1 hour 10 minutes, rotating the pan every 20 minutes.
RIGHT BEFORE THE SQUARES ARE DONE BAKING, MAKE THE GLAZE: In a medium bowl, whisk together the confectioner's sugar, water, and vanilla until smooth.
Remove the pear squares from the oven and set the baking sheet over a wire rack. Drizzle the glaze evenly over the top and let cool completely, about 4 hours. Once cooled, cut into 24 squares. The squares keep, covered, for 1 week in the refrigerator or for 4 to 6 months in the freezer, tightly wrapped.