Make the pie dough. In a large bowl, whisk together the flour, salt, and 2 teaspoons sugar. Add the cold cubed butter and use a pastry cutter or your fingers to work it in until the mixture looks like rough crumbs with some flat, pea-sized butter pieces remaining. Drizzle in ice water 1 tablespoon at a time, tossing with a fork after each addition, until the dough just comes together when you press a handful. You may not need all the water. Divide the dough into two equal portions, flatten each into a rectangle about 1 inch thick, wrap in plastic wrap, and refrigerate for at least 30 minutes.

While the dough chills, make the filling. Toss the sliced apples in a large bowl with the 3/4 cup granulated sugar, 3 tablespoons flour, cinnamon, nutmeg, allspice, salt, and lemon juice until evenly coated. Spread the apples on a clean kitchen towel or layers of paper towels and pat them dry for a couple of minutes to pull out excess moisture. This step keeps your bottom crust from getting soggy.

Preheat your oven to 400 degrees F. On a lightly floured surface, roll one dough rectangle out to roughly 20x15 inches, large enough to cover the bottom and come slightly up the sides of your 18x13 inch sheet pan. Carefully transfer it to the ungreased sheet pan by rolling it loosely around your rolling pin and unrolling it over the pan. Press it into the corners and up the sides without stretching it. Trim the overhang to about 1/2 inch around the rim.

Spread the dried apple filling evenly over the bottom crust, leaving a 1/2-inch border around the edges. Scatter the small pieces of butter over the apples.

Roll the second dough rectangle to the same 20x15 inch size. Drape it over the filling by rolling it onto your rolling pin and unrolling it across the top. Press the edges of the top and bottom crust together and crimp them by folding the edge under itself and pressing down with a fork or your fingers all the way around. Cut several slits or small vents across the top crust to let steam escape during baking.

Brush the top crust evenly with the egg wash using a pastry brush, then sprinkle coarse sugar over the entire surface.

Bake for 40 to 45 minutes, until the crust is a deep golden brown and you can see the filling bubbling through the vents. If the edges are browning too fast before the center is done, tent those edges loosely with small strips of foil.

Transfer the pan to a wire rack and cool for at least 30 minutes before slicing. Use a sharp knife or a pizza cutter to slice into rectangles, about 4 columns by 5 rows for 20 pieces. Serve warm or at room temperature.