In a large mixing bowl, combine first 6 ingredients; add apples, tossing to combine. Set apple mixture aside. Adjust oven rack to lowest position; place a rimmed baking sheet on the rack and preheat oven to 425°. Line a 9" deep-dish pie pan with one crust; fill with apples. Top with the second crust, tucking top crust under the edge of the bottom crust; pinch crusts together to seal. Flute edge of crust with fingers. Cut 6-8 slits in the crust; brush with egg and sprinkle with sugar. Place pie on the preheated baking sheet; bake until the crust is a dark golden-brown (40-45 min.), covering the edges of the crust with strips of foil to prevent overbrowning in last 10-15 min., if needed. Transfer pie to a wire rack; cool 2 hrs. before serving.