Heat the oven to 425°F. Place one refrigerated crust in a 9-inch pie plate and gently press it across the bottom and up the sides. Keep the second crust refrigerated until you are ready to cover the filling.

In a large bowl, combine the peeled, cored, thinly sliced apples with the sugar, flour, cinnamon, salt, and lemon juice. Toss until every apple slice is evenly coated, then let the mixture stand for about 5 minutes.

Pour the apples and any juices that have collected in the bowl into the bottom crust. Spread the apples into an even mound and arrange the small butter pieces over the top.

Cover the filling with the second crust. Trim excess dough, crimp the edges to seal, and cut 4–6 vents in the top crust so steam can escape.

Beat the egg with the water and brush the mixture over the top crust. Sprinkle with coarse sugar, if using.

Bake at 425°F for 15–20 minutes. Reduce the oven temperature to 375°F and continue baking for another 35–45 minutes, until the crust is golden brown and the filling is visibly bubbling through the vents.

If the edges brown too quickly, cover them loosely with aluminum foil while the center finishes baking. Transfer the pie to a rack and cool for at least 2 hours before slicing so the filling can set.