1. In a large, heavy-bottomed saucepan, melt butter over medium heat. Stir in apples, lemon juice, granulated sugar, cinnamon, and salt; cover and cook until apples have softened but are not falling apart, about 8 minutes. Add flour and cook, uncovered, until juices have thickened, about 2 minutes. Transfer to a 9-by-13-inch baking dish; let cool completely.

2. On a lightly floured piece of parchment, roll out 1 disk of dough into a 13-inch round, about 1/8 inch thick. Fit into a 9-inch pie dish. Refrigerate until firm, at least 30 minutes. Meanwhile, roll out remaining disk of dough on a lightly floured piece of parchment to a 13-inch round, about 1/8 inch thick. Transfer on parchment to a baking sheet. Refrigerate until firm, about 30 minutes.

3. Place apple mixture in prepared pie dish; spread in an even layer. Lightly brush rim of bottom dough with water.

4. For top dough, use a 2 1/4-inch diamond cookie cutter to stamp out 16 diamonds (reroll scraps, if needed). Freeze cut shapes on parchment-lined baking sheets until very firm, 15 minutes. Trim bottom dough flush with pie-dish rim. In a small bowl, whisk egg white and 1/2 tablespoon water with a fork. In another small bowl, whisk egg yolk and 1/2 tablespoon water. With a small pastry brush, brush every other tile with egg white and sprinkle with sanding sugar. Brush remaining tiles with yolk. Starting in center of pie, arrange diamonds over filling, alternating between egg-wash finishes. Using kitchen shears, trim diamond edges flush with pie-dish rim. Refrigerate until dough is firm, 30 minutes.

5. Preheat oven to 400 degrees with a rack in lower third and a foil-lined baking sheet below. Place dish directly on rack; bake until crust is just beginning to brown, about 20 minutes. Reduce oven temperature to 375 degrees; bake until crust is golden brown and juices are bubbling in center, 1 hour to 1 hour, 10 minutes. (If crust is browning too quickly, tent with foil.) Transfer to a wire rack; let cool completely, at least 6 hours.