1. For crust: Combine first 4 ingredients; cut in shortening until mixture resembles coarse meal. Add apple juice, 1 tablespoon at a time, tossing until dough is moist and begins to stick together. Cover in plastic wrap; chill 30 minutes.
2. Preheat oven to 400°.
3. For filling: Toss apples with lemon juice. Whisk together next 4 ingredients; pour over apples, tossing until well-combined.
4. Unwrap dough; place on parchment paper. Roll into a 15-inch circle. Place dough and parchment on rimmed baking sheet; arrange apples in center, leaving 2-inch border. Fold edges in; press gently to seal. Dot apples with butter.
5. Whisk egg white and water. Brush dough with egg wash; sprinkle with coarse sugar. Loosely cover with foil; bake 25–30 minutes. Uncover; bake 10 minutes or until tender and golden.
6. Let stand 20 minutes. Cut into 8 wedges; serve.