• Preheat oven to 400 degrees F. Center rack in oven.

MAKE THE APPLE PIE FILLING:

• In a small bowl, combine the sugars, cornstarch, spices and salt.
• In a large bowl, toss together the apples, dulce de leche, apple cider and vanilla extract. Add the dry ingredients and toss to combine.

PIE CRUST:

• Between waxed paper, roll out pie dough as large as possible keeping it a good thickness. Line the deep dish pie pan with crust and let it hang over the sides. Brush with egg white mixture. Add the apple filling and spread it out evenly.
• Roll out the 2nd crust a little bit too and place it on top of the pie. Crimp the edges together in a decorative fashion to seal. Brush with the egg white mixture. Cut a few holes in the top crust for venting. Sprinkle with coarse sugar, if using.
• Bake for 30 minutes. Then turn the temperature down to 375 degrees F. If the pie is browning too much, cover it with foil and top with a pie-crust-shield to prevent the crust edges from burning. If you don’t have a pie shield, just cover the whole thing with foil. Bake for another 30 minutes.
• Remove the pie from the oven and cool on a rack for several hours to allow the filling to set.