Prepare the Pie Dough: In a large bowl, whisk together flour and salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized butter pieces remaining. Gradually add ice water, 1 tablespoon at a time, mixing until the dough just comes together. Divide the dough in half, wrap each disk in plastic wrap, and chill for at least 1 hour.

Prepare the Apricot Filling: In a separate large bowl, gently toss the halved apricots with granulated sugar, cornstarch, lemon juice, almond extract, and cinnamon until evenly coated. Set aside while you roll out the crust.

Assemble the Bottom Crust: Preheat your oven to 400°F (200°C). On a lightly floured surface, roll out one dough disk into a 12-inch circle. Carefully transfer the dough to a standard 9-inch pie plate. Trim the edges, leaving about a 1-inch overhang.

Fill and Top the Pie: Pour the apricot filling into the bottom crust. Dot the top of the filling with the small pieces of butter. Roll out the second dough disk and place it over the filling. Crimp the top and bottom edges together to seal. Cut several slits in the top crust for venting steam.

Bake the Pie: Brush the top crust evenly with the egg wash (yolk mixed with water). If desired, sprinkle lightly with coarse sugar. Place the pie on a baking sheet and bake at 400°F (200°C) for 15 minutes. Then, reduce the oven temperature to 375°F (190°C) and continue baking for an additional 45-50 minutes, or until the crust is golden brown and the filling is bubbly.

Cool Completely: Allow the pie to cool on a wire rack for at least 3 to 4 hours before slicing and serving. This allows the filling to set properly.