Reducing already-sweet apple cider into a syrup adds concentrated flavor to this pie and sweetens it with less than half the added sugar of a typical apple pie recipe.
To prepare crust: Whisk all-purpose flour, whole-wheat flour and 1/2 teaspoon salt in the bowl of a stand mixer. Add butter; toss to coat. Refrigerate for 30 minutes. Mix with the paddle attachment on low speed until the butter forms almond-size pieces, 2 to 3 minutes. Add oil; mix for 15 seconds. Add 6 tablespoons water and mix until the dough just comes together. Add more water, 1 tablespoon at a time, if it seems dry. (Alternatively, combine the flours and salt in a food processor; pulse several times. Add butter and refrigerate for 30 minutes. Pulse until almond-size pieces form. Add oil and pulse several times. With the motor running, gradually add just enough water until the dough comes together.) Divide the dough in half and shape each piece into a 5-inch disk. Wrap each in plastic wrap and refrigerate for 1 hour.
To prepare filling: Place cider in a small saucepan and bring to a boil over medium-high heat. Reduce heat to medium and boil until reduced to 1/2 cup, 25 to 30 minutes. Let cool.
Meanwhile, position racks in center and bottom of oven; preheat to 425°F. Line a baking sheet with parchment paper or foil.
Whisk cornstarch, granulated sugar, cinnamon, allspice, nutmeg and salt in a small bowl. Combine apples, lemon juice and the reduced cider in a large bowl.
Roll 1 dough disk out on a lightly floured surface into a 12-inch round. Transfer to a 9-inch (not deep-dish) pie pan. Trim dough flush with the pan rim. Freeze for 15 minutes. Roll the second disk into a 12-inch round. Use a 21/4-inch cutter to cut 26 diamonds (reroll scraps, if needed). Chill until ready to assemble the pie.
Toss the spice mixture with the apples to coat. Spoon into the crust. Brush every other diamond with egg wash and sprinkle with sugar. Starting in the center, arrange diamonds over the filling, alternating the finishes. Trim edges flush with the rim. Refrigerate for 30 minutes.
Place the pie on the center rack with the baking sheet on the rack below. Bake for 10 minutes. Reduce oven temperature to 350°. Bake until golden and bubbling, 50 to 60 minutes. Let cool on a wire rack for 1 hour before serving.
Refrigerate dough (Step 1) for up to 2 days or freeze for up to 6 months.
9-inch (not deep-dish) pie pan, parchment paper, 2 1/4-inch diamond cutter