To prepare pastry dough, combine first 5 ingredients in the bowl of a food processor, and pulse 2 times. Add 1/4 cup butter and shortening, and pulse 4 times, or just until mixture resembles coarse crumbs.
Transfer flour mixture to a large bowl. Add ice water, 1 tablespoon at a time, tossing with a fork just until moistened. Gently gather dough into a ball. Divide dough in half, and press each portion into a 4-inch circle. Wrap each portion in plastic wrap, and chill 30 minutes.
Preheat oven to 375°F.
While the dough chills, prepare the filling. Combine peaches, 6 tablespoons granulated sugar, 1/4 cup all-purpose flour, lemon juice, cinnamon, nutmeg, and 1/8 teaspoon salt. Set aside.
Remove 1 portion of dough from refrigerator. Place dough between 2 sheets of plastic wrap, and roll dough into a 12-inch circle. Refrigerate 15 minutes, or until plastic can be removed. Repeat with remaining dough portion.
Remove top sheet of plastic from 1 dough portion. Place dough, plastic side up, in a 9-inch glass or ceramic pie plate (not deep dish) coated with cooking spray. Remove top sheet of plastic wrap, allowing ends of dough to extend over sides of pie plate. Spoon peach mixture into pie plate, and dot with pieces of butter. Whisk together egg white and 1 teaspoon water. Lightly brush edges of dough with egg white mixture.
Remove plastic from remaining portion of dough, and gently place dough over pie. Seal edges of dough and flute. Lightly brush top of dough with egg white mixture, and sprinkle with 1 tablespoon turbinado sugar. Cut 6 slits in top of pie to allow steam to escape.
Bake for 50 to 55 minutes, or until pastry is golden brown, and filling is bubbly. Lightly shield edges of pie with foil during last 10 minutes, if necessary. Cool completely on a wire rack.