How to Make It
To prepare crust, weigh or lightly spoon flour into dry measuring cups; level with a knife. Place flour, baking powder, and salt in the bowl of a food processor, and process to combine. Cut butter and shortening into 1/2-inch pieces; add to processor bowl. Pulse 2 to 3 times or until butter is about the size of dried peas. Sprinkle vinegar and ice water over mixture. Pulse 2 to 3 times or until mixture resembles coarse sand.
Scrape mixture onto a lightly floured work surface. Press mixture into a ball; divide into 2 equal pieces. Press each half into a 4-inch disk. Cover each disk with plastic wrap, and chill 30 minutes. (The dough can be made 1 day ahead. If it's chilled for 24 hours, let it stand at room temperature for 10 minutes before rolling.)
Preheat oven to 425°.
To prepare filling, place apples and juice in a large bowl; toss to coat. Combine brown sugar and next 5 ingredients (through 1/4 teaspoon salt) in a small bowl. Sprinkle apples with brown sugar mixture; toss well to combine.
Unwrap 1 dough disk, and place on a lightly floured work surface. Roll to an 11-inch circle. Place into a 9-inch pie plate lightly coated with baking spray. Pour filling into prepared pie plate (dish will be very full). Arrange diced butter on top of filling. Roll remaining half of dough into a 10-inch circle on a lightly floured surface. Place dough on top of pie; fold edges under, and flute decoratively. Cut slits in top of dough to allow steam to escape. Lightly brush top of dough with egg white. Sprinkle with granulated sugar.
Bake at 425° for 15 minutes; reduce oven temperature to 350°. Bake an additional 1 hour or until golden and bubbly. Shield edges of pie with foil if necessary. Place pie on a wire rack; cool completely before slicing.