PreparationFor crust: Blend flour, sugar, and salt in processor 5 seconds. Add butter. Using on/off turns, blend until butter is reduced to small pea-size pieces. Add 4 tablespoons orange juice. Blend, using on/off turns, until moist clumps form, adding more juice by teaspoonfuls if dough is dry. Gather dough into ball; flatten into disk. Wrap in plastic and chill at least 1 hour. DO AHEAD: Can be made 1 day ahead. Keep chilled. Roll out dough on floured surface to 14-inch round. Transfer to 10-inch-diameter glass pie dish. Cut off all but 1/2 inch of dough overhang. Fold dough edge under and crimp decoratively, forming high-standing rim. Freeze 10 minutes. DO AHEAD: Can be made 1 day ahead. Cover and refrigerate crust. Brush inside of crust with enough beaten egg white to coat. For apples: Preheat oven to 350°F. Whisk brown sugar and butter in large ovenproof skillet over medium heat until butter melts, sugar dissolves, and mixture comes to boil. Boil 1 minute, whisking constantly. Remove from heat. Arrange apples, rounded side down, in syrup. Bake 15 minutes; turn over. Bake until just tender, about 20 minutes longer. Transfer apples to paper towels to cool slightly. Whisk syrup in skillet until smooth. Cool slightly and reserve. Maintain oven temperature. For filling: Mix sugar, flour, and salt in small bowl. Place eggs in medium bowl. Gradually whisk in reserved syrup from apples. Add corn syrup, vanilla, and sugar mixture; whisk until smooth. Stir in pecans. Pour filling into crust. Arrange apples, rounded side up, atop filling. Bake pie until filling is set in center, covering edges with foil if browning too quickly, about 1 hour 20 minutes. Transfer to rack and cool completely. DO AHEAD: Can be made 1 day ahead. Cover loosely with foil and let stand at room temperature.
PreparationFor crust: Blend flour, sugar, and salt in processor 5 seconds. Add butter. Using on/off turns, blend until butter is reduced to small pea-size pieces. Add 4 tablespoons orange juice. Blend, using on/off turns, until moist clumps form, adding more juice by teaspoonfuls if dough is dry. Gather dough into ball; flatten into disk. Wrap in plastic and chill at least 1 hour. DO AHEAD: Can be made 1 day ahead. Keep chilled. Roll out dough on floured surface to 14-inch round. Transfer to 10-inch-diameter glass pie dish. Cut off all but 1/2 inch of dough overhang. Fold dough edge under and crimp decoratively, forming high-standing rim. Freeze 10 minutes. DO AHEAD: Can be made 1 day ahead. Cover and refrigerate crust. Brush inside of crust with enough beaten egg white to coat. For apples: Preheat oven to 350°F. Whisk brown sugar and butter in large ovenproof skillet over medium heat until butter melts, sugar dissolves, and mixture comes to boil. Boil 1 minute, whisking constantly. Remove from heat. Arrange apples, rounded side down, in syrup. Bake 15 minutes; turn over. Bake until just tender, about 20 minutes longer. Transfer apples to paper towels to cool slightly. Whisk syrup in skillet until smooth. Cool slightly and reserve. Maintain oven temperature. For filling: Mix sugar, flour, and salt in small bowl. Place eggs in medium bowl. Gradually whisk in reserved syrup from apples. Add corn syrup, vanilla, and sugar mixture; whisk until smooth. Stir in pecans. Pour filling into crust. Arrange apples, rounded side up, atop filling. Bake pie until filling is set in center, covering edges with foil if browning too quickly, about 1 hour 20 minutes. Transfer to rack and cool completely. DO AHEAD: Can be made 1 day ahead. Cover loosely with foil and let stand at room temperature.