1. Chop frozen butter into ½ inch pieces. Return to freezer. Add vinegar to ice water and place in refrigerator.
2. Add all dry crust ingredients to food processor bowl with blade attachment. Pulse a few times to combine ingredients. Add cold butter and pulse until you see pea sized chunks of butter (about 10-15 pulses). Pour ice water/vinegar into mixture and pulse again, until the dough sticks together (about 10 pulses). It will look crumbly but not sandy or dusty.
3. Place a large sheet of plastic wrap (about 16 in long) on a counter. Transfer dough flattened plastic wrap and form into a ball, pressing any flour bits into dough. Cut ball in half and form two discs, about 5 inches each. Place 2nd disc on another sheet of plastic wrap (about 16 in long). Wrap each disc with plastic and refrigerate for 1-2 hours.
4. Right after refrigerating dough, prepare filling by peeling and slicing apples, transfer to large mixing bowl. Add granulated sugar, brown sugar, cinnamon, and salt to apples. Stir cinnamon sugar mixture into apples so all apples are covered. Cover and leave out on counter for at least an hour.
5. After about an hour (or just before you plan on assembling the pie), stir apples and pour juice into a small saucepan over medium-high heat, cook until apple juice is reduced by about ½ (you can also heat it up in the microwave). Remove, and add back to apples. Mix apples and cinnamon sauce together. Sprinkle cornstarch and flour mixture over apples and stir all together until apples are evenly coated.
6. Grab a ceramic or glass pie pan, place next to counter where you will roll out your dough. Remove one crust disc from fridge and roll out into a 12 inch circle on the plastic wrap. This way you don’t have to add extra flour to prevent sticking. Transfer to pie pan, then pour filling into pan, spread filling out so it’s even. Place pie in freezer and grab the other crust disc. Roll top crust out as you rolled out the bottom crust.
7. Grab pie from freezer and gently drape the top crust over the filling. Smooth out the top crust. Cut crust off that extends over pie pan lip. Crimp edge with a fork and pierce 4-5 long slits in the top crust. Return to freezer and preheat oven to 425 degrees.
8. While oven is preheating, and pie is in the freezer, whisk egg and water in a small bowl. Set aside until oven is ready.
9. Once oven is preheated, remove pie from freezer and brush egg over crust. Sprinkle sugar evenly over crust. Place in oven and bake at 425 degrees for 15 minutes. Then decrease oven temperature to 375 and bake for 50-60 minutes. Cover edges with foil if it gets too brown.
10. Once crust is browned and filling is bubbling, remove from oven and let it rest for at least 1-2 hours.
11. Serve plain, with vanilla ice cream or with caramel sauce.