Carefully remove rind from oranges using a vegetable peeler, making sure to avoid white pithy part of rind (reserve oranges for another use). Cut rinds into 1 x 1/8-inch-wide strips. Combine water, honey, and lemon juice in a small saucepan; bring to a boil over medium-high heat. Add orange rind; cover, reduce heat, and simmer 30 minutes or until rind is very soft. Remove rind from pan with a slotted spoon; discard cooking liquid.
Preheat oven to 350°.
Combine brown sugar, flour, cinnamon, ginger, and salt in a large bowl. Add apples; toss well to coat. Fit 1 portion of dough into a 9-inch deep-dish pie plate coated with cooking spray, allowing dough to extend over edge of plate. Spoon half of apple mixture into crust; arrange orange rind mixture over top. Spoon remaining apple mixture over top. Place remaining dough on apple mixture. Press edges of dough together. Fold edges under; flute. Cut 3 (1-inch) slits in top of pastry using a sharp knife. Brush the top and edges with the beaten egg.
Place pie on a baking sheet; bake at 350 degrees for 1 hour or until golden. Cool on a wire rack.