To make the dough, combine the flour, sugar and salt in the bowl of a food processor and pulse the mixture several times to combine.
Add the cold butter and pulse again for about 30 seconds. Add the shortening and process until the mixture resembles coarse meal. Sprinkle in the water and mix until the dough is moistened.
Turn the dough out into a large bowl and shape into a large ball. Remove 1/3 of the large ball and wrap in plastic wrap; wrap the remaining dough (2/3s of original size) in plastic wrap as well, pressing down each to form a disk. Refrigerate both disks for at least 30 minutes or up to 2 days.
To make the filling, combine all of the ingredients in a large mixing bowl. Mix thoroughly until some of the juices from the fruit are released. Set aside.
Preheat the oven to 400°F/205°C.
Using a paper towel or mister, apply a thin coat of vegetable oil to the inside of a 9x13-in. cake pan.
To assemble the pie, dust a work surface and rolling pin with flour. Roll the larger piece of dough into a rectangle, approximately 10x14-in. Roll the dough back onto the rolling pin then gently unroll onto the bottom of the prepared pan.
On a baking sheet that will fit into the freezer and dusted with flour, roll the remaining piece of dough into a rectangle, approximately 10x14-in. Trim the rough edges . Cut the rectangle into 12 (13-in. long) strips then place the pan in the freezer for 10 - 15 minutes.
Spoon the filling into the pastry-lined pan in an even layer. Lay the dough strips on top of the fruit in a lattice pattern. Use your fingers to pinch the edges of the dough strips and the bottom dough layer together. Sprinkle the top of the pie with 1 Tbsp. sugar.
Bake the pie on the second to lowest rack position of the oven for 35 - 40 minutes or until the filling is bubbly and the pastry is golden. Cool the pie to allow the filling to gel, then serve.