Prepare the Filling: Whisk together sugar and cornstarch in a saucepan. Whisk in 1/2 cup water, ginger, and salt; bring to a boil over medium-high, whisking often. Cook, whisking constantly, until thickened, about 1 minute. Remove pan from heat. Stir in blueberries and lemon juice, lightly crushing half of the blueberries; let stand until completely cool, about 30 minutes.

Prepare the Dough: Place flour and salt in the bowl of a food processor; pulse until combined, about 3 times. Scatter shortening and butter over top of flour mixture; pulse until mixture resembles coarse crumbs, 6 to 7 times. Add 1/2 cup of the ice water; pulse until mixture just starts to clump together, about 8 times, adding additional water, 1 tablespoon at a time, if necessary. Scrape out onto a lightly floured surface. Knead until it comes together, 2 to 3 times. Divide in half, and shape each half into a flat disk; wrap disks with plastic wrap, and chill about 30 minutes.

Roll one Dough disk to 1/8-inch thickness; cut 6 (5-inch) circles, and discard scraps. Repeat procedure with remaining disk. Scoop about 1 rounded tablespoon Filling into center of each circle. Moisten edge of half of each circle with water; fold circles in half, and crimp edges to seal. Cover and chill until ready to fry.

Pour vegetable oil to a depth of 1 inch in a large, deep skillet; heat oil to 360°F. Place 3 to 4 pies in hot oil, and fry until golden brown on both sides, 6 to 7 minutes, turning occasionally. Remove pies to paper towels to drain; sprinkle with powdered sugar. Repeat procedure with remaining pies and powdered sugar. Serve warm or at room temperature.