Preheat the oven. Arrange the oven racks so that one rack is in the center and another is below it. Place an empty baking sheet lined with aluminum foil on the lower rack to catch any drips from the pie. Preheat the oven to 400°F (200°C).
Prepare the pie crust. Roll out both prepared pie crusts. Then, line the pie plate with the bottom crust, trimming any excess.
Prepare the filling. In a large mixing bowl, combine the apples, peaches, brown sugar, granulated sugar, flour, cinnamon, and salt. Mix well. Pour the filling into the prepared pie crust. Dot the top of the filling with small pieces of butter.
Place the top crust on, and brush with egg and cinnamon sugar. Lay the top crust on top of the fruit, or layer on lattice strips if using. If you choose to use a solid top crust, be sure to cut many slits in the top to allow moisture to escape. Brush the crust with a beaten egg. Combine cinnamon and sugar for the crust in a small bowl and sprinkle generously on top.
Bake. Place the pie on the center rack. Then, bake in the preheated oven for 40 minutes. Check the pie after 20 minutes. Cover the edges with a pie shield or aluminum foil if they are browning too quickly.
Cool at least 3 hours before serving. Allow the pie to cool for at least 3 hours before serving. For best results, chill the pie in the refrigerator for 3 hours or overnight.