Melt the butter in a large pot over medium-low heat. Add the apples, brown sugar, flour, cinnamon, lemon juice, and salt. Stir together and cook, stirring occasionally, until the apples soften, 8 to 10 minutes. Remove from the heat and set aside to cool.

Meanwhile, divide the prepared pie dough in half (if not already in 2 discs) and lightly flour a work surface. Roll one disc of dough out to around 1/8-inch thick, (a bit larger than your pie plate). Transfer the rolled sheet of dough into the pie plate, gently pushing it in to the bottom.

Transfer the cooled cooked pie filling into the prepared crust. Roll the other disc of pie dough out onto a lightly floured surface and transfer on top of the pie. Alternately, you can cut the rolled pie dough into strips using a pizza cutter and braid the top layer. Cut vents in the pie crust if not braiding. Trim the excess dough hanging over the sides and crimp the edges of the pie with your fingers to seal.

Lightly brush the top of the pie with the egg wash and sprinkle evenly with coarse sugar, if desired. Bake the pie for 15 minutes at 425 F, reduce the temperature to 350 F, and continue baking until golden brown and the apple pie filling bubbles through the vents, around 40 minutes. Place a piece of aluminum foil over the pie during the cooking process if the crust starts to get too brown. Set aside to cool before serving.