Sift the flour, sugar and salt into a large mixing bowl. Using your fingertips or a pastry cutter, work the butter and shortening into the flour until the mixture resembles small peas. Work the ice water into the mixture with your fingers just until the dough comes together; be careful not to overmix.
Form the dough into 2 disks, and wrap each disk individually in plastic wrap. Refrigerate for at least 1 hour or overnight.
Roll out and fit into pans and use for pies as desired. Makes 2 (9-inch) pie crusts
For the pie:
Roll 1 piece of the pastry out to a thickness of between 1/8 and 1/4-inch and fit into a deep-dish pie pan. Trim the overhang to about 1-inch, then fold pastry overhang inward along the top edge of the pie pan, press, and crimp the top edges decoratively (so that the crust is thicker along the top edge and stands up slightly above the top edge of the pie pan). Place in the refrigerator for at least 30 minutes and up to several hours.
Preheat the oven to 400 degrees F.
Line the pie crust with parchment paper and fill with pie weights. Place in the oven and bake until the top edges are lightly golden and the bottom of the crust is set and no longer looks doughy, usually about 20 minutes. Remove from the oven, remove paper and weights and set aside to cool. Reduce oven temperature to 375 degrees F.
Spread the pecan pieces along the bottom of the par-baked crust. Toss the chocolate chips in a little flour just to coat, then spread them evenly among the pecan pieces.
Combine the eggs, sugar, brown sugar, cane syrup, corn syrup, vanilla, salt, butter, and remaining tablespoon of flour in a mixing bowl. Mix well. Pour the mixture over the pecans and chocolate chips.
Bake until the filling sets and pastry is nicely browned, usually about 1 hour.
Transfer to a cooling rack and allow pie to cool at least 30 minutes before serving. Serve warm or at room temperature.