In a large bowl, toss apples. In a smaller bowl, mix together 1/2 cup sugar, the flour, candied ginger, fresh ginger, lemon peel, ground ginger, and cinnamon. Stir sugar-and-spice mixture into apples, tossing to coat well. Place apple mixture in chilled pie shell. Arrange cutout acorns and leaves over pie in a random pattern, leaving some areas uncovered. Whisk egg white with 1 tablespoon water, brush over top of crust, and sprinkle crust with remaining 1 tablespoon sugar. Bake 20 minutes.