In a large bowl, mix together the flour, salt, and 1 tablespoon of sugar.
Add the chilled, cubed butter to the flour mixture. Use a pastry cutter or your fingers to work the butter into the flour until the mixture resembles coarse crumbs.
Divide the dough into two equal parts, shape each into a disk, wrap in plastic wrap, and chill in the refrigerator for at least 1 hour.
In a large bowl, combine the sliced apples, 3/4 cup sugar, 2 tablespoons flour, cinnamon, nutmeg, and lemon juice. Toss until the apples are evenly coated.
On a lightly floured surface, roll out one disk of dough into a circle large enough to line a 9-inch pie dish. Place the dough into the pie dish, pressing it gently against the bottom and sides.
Roll out the second disk of dough and place it over the apple filling. Trim any excess dough and crimp the edges to seal the pie.