Make the dough ahead of time and get it out of the way.
Weigh out your flour and mix it with the sugar and salt. Put in the food processor.
Add chunks of butter and pulse just until mixture is coarse. Don’t overdo it! Add cold water 2 tablespoons at a time and pulse until mixture holds together when you pinch it. Empty onto a pastry mat and push together into a big ball. Wrap tightly and chill until ready to use. While the crust is chilling, make the filling.
Spread the apples in a large roasting pan and toss with 2 tablespoons of white sugar. Set roasting pan under broiler so that apples are about 6 to 7 inches underneath and broil for about 6 to 8 minutes or just until apples are softened and aromatic. Remove from heat and stir in brown sugar, flour, cinnamon and lemon juice, then toss in the butter and stir until well mixed. Set the filling aside to cool while you roll out your crusts.
On a very well floured pastry mat, roll pie dough into a large circle and drape it over the sides of the pan. Press to fit.
Spoon apples from the apple filling into the pan, drizzling the liquid over the apples and pressing the apples down tightly.
Roll the second half of pie dough into a large circle and lay it over the apples. Press the top and bottom sections of pie dough together, trim, turn down edges and crimp. Brush with a little egg wash and sprinkle with coarse sugar.
Preheat oven to 400 degrees F. Place a foil lined rimmed baking sheet in the oven to heat the sheet.
Set the pie on the hot baking sheet and bake for 30 minutes at 400 degrees F. At this point, crust should be golden brown (though you can check earlier). Cover loosely with foil and bake for another 15 minutes for a total of 45 minutes.