In a large bowl, whisk together the flour and salt. Add the cold, cubed butter and use a pastry blender to cut it in until the mixture resembles coarse crumbs with pea-sized pieces of butter still visible.

Gradually sprinkle in the ice water, tossing with a fork until the dough begins to clump together. Do not overmix.

Divide the dough in half, shape each into a 1-inch thick disk, wrap in plastic wrap, and refrigerate for at least 1 hour.

Preheat your oven to 425°F (220°C). Place a baking sheet on the lowest rack to preheat as well.

In a large bowl, toss the sliced apples with lemon juice. In a small bowl, mix the granulated sugar, brown sugar, flour, cinnamon, nutmeg, and allspice. Pour this mixture over the apples and toss to combine.

On a floured surface, roll one disk of dough into a 12-inch circle and fit it into a 9-inch pie plate. Spoon the apple filling into the crust and dot with the 2 tablespoons of butter.

Roll out the second disk of dough. Place it over the pie or cut it into strips for a lattice top. Trim, fold, and crimp the edges to seal. Brush the top crust with the egg wash and sprinkle with coarse sugar, if desired.

Place the pie on the preheated baking sheet. Bake for 15 minutes. Then, reduce the oven temperature to 375°F (190°C) and continue to bake for 40-50 minutes, or until the crust is golden and the filling is bubbly. Cover edges with foil if they begin to over-brown.

Let the pie cool on a wire rack for at least 4 hours before slicing and serving. This allows the filling to set.