Position a rack in the lower third of the oven and preheat to 425 (F).
On a lightly floured surface, roll out one of the pie dough disks into a rough 12-inch circle about 1/8 to 1/4-inch thick. Transfer the circle to a 9-inch pie pan and store in the refrigerator while you prepare the rest of the pie.
Next, make the lattice top. Roll out the other disk into a 12-inch circle about 1/8 to 1/4-inch thick. Cut into strips. Transfer the strips to a baking sheet and refrigerate while you prepare the filling.
Peel and core 2 1/2 pounds of pears and slice them into 1/4-inch slices. Transfer the slices to a large bowl along with 1/4 cup granulated sugar, 1/4 cup all-purpose flour, 1/2 teaspoon ground cinnamon, 1/4 teaspoon freshly grated nutmeg, 1/4 teaspoon ground allspice and juice from 1/2 lemon. Stir gently to combine.
Add half the pears to the pie shell, and drizzle 1/4 cup of the crème fraîche caramel over the top, then add the remaining pears. Drizzle the remaining caramel on top. Lay out the prepared pie dough strips for the lattice and carefully weave a lattice. Trim off any excess lattice too long for the pie plate and fold the edges of the bottom crust up and over the lattice strips. Crimp the edges together. Slide the whole pie into the freezer until the crust is very firm, about 15 minutes, before baking.
When the pie dough is firm, it's ready to be baked. Place the pie on a rimmed baking sheet to catch any drips. Beat 1 large egg in a small bowl, then use a pastry brush to brush the top of the pie with egg wash. Sprinkle the egg wash with 1 tablespoon turbinado sugar.
Bake the pie until it is deep golden brown and the juices are bubbling, 45 to 55 minutes. If the crust begins to burn before the filling bubbles, tent it with aluminum foil. Cool slightly before serving. The pie is best the day it's made.