You will need a deep-dish pie pan (about two inches deep) for this pie. This is one of the few pies that are better served cold than warm..Plus: More Dessert Recipes and Tips
In a food processor, combine 1 cup of the flour, the butter, egg, and sugar. Pulse 10 to 15 times, or until the mixture is a fairly smooth paste. Add the remaining 1 cup flour and pulse until the dough comes together. Do not overwork. Form the dough into a ball, flatten into a disk, wrap in wax paper and refrigerate for at least 2 hours or overnight.
On a lightly floured sheet of parchment paper, roll out the dough into a 13-inch round, about 1/8 inch thick. Transfer the dough to a 10 1/2-inch deep-dish pie plate and fit it against the bottom and sides without stretching. Trim the overhanging dough to 1/2 inch, fold it under and crimp decoratively. Using a fork, prick the bottom and sides of the pie shell all over. Freeze the pie shell until firm, 10 to 15 minutes.
Preheat the oven to 400°. Bake the pie shell for 10 minutes, or until just beginning to turn golden around the edges. Transfer to a rack to cool to room temperature. Leave the oven on.
Halve each squash and, using a spoon, scoop out and discard the seeds. Place the squash, cut sides up, in a large baking dish. Pour 1/2 inch of water into the dish. Place 2 tablespoons of the brown sugar and 1 tablespoon of the butter in each squash cavity. Cover the dish with foil and bake the squash for 45 minutes, or until it is soft when pricked with a fork.
Using a spoon, scoop the squash flesh into a food processor, along with any cooking juices. Puree until smooth. Add the remaining 3/4 cup brown sugar and the ginger and salt. Pulse several times to mix. Remove the food processor cover and let the puree cool for about 10 minutes. Add the eggs 1 at a time, pulsing until incorporated between each addition.
Using a small sharp knife, peel, quarter and core the pears. Slice them lengthwise 1/8 inch thick. Arrange the pear slices in the bottom of the cooled pie shell. Mix the granulated sugar and cinnamon and sprinkle on top of the pears. Pour the squash filling over the pears and smooth the surface with a spatula.
Bake the pie in the lower part of the oven for 15 minutes. Lower the temperature to 350° and bake for 40 to 50 minutes longer, or until the crust is golden brown and the filling is just set. (The center of the filling will continue to cook after the pie is removed from the oven). Transfer to a rack to cool completely before serving.