1. To prepare crust: Whisk whole-wheat flour, all-purpose flour and salt in the bowl of a stand mixer. Add 4 tablespoons butter. Refrigerate until firm, 30 minutes to 1 hour.
2. Mix on low speed with the paddle attachment until the butter forms almond-size pieces, 2 to 3 minutes. Add oil and mix for 30 seconds to incorporate. Add 3 tablespoons water and mix until the dough just comes together, with flecks or streaks of butter. Add up to 1 tablespoon water if it seems dry. Form the dough into a disk, wrap in plastic wrap and refrigerate for at least 1 hour or up to 2 days.
3. Preheat oven to 375°F. If the dough has been refrigerated for more than 1 hour, let it stand at room temperature for 20 minutes. Roll the dough out on a lightly floured surface to a 12½-inch round. Transfer to a 9-inch deep-dish pie pan. Crimp the edges. Freeze the lined crust for 15 minutes.
4. Line the crust with parchment paper and fill with pie weights (or dried beans). Bake until the edges are golden brown, about 15 minutes. Remove the paper and pie weights. Bake until the crust is golden brown, about 10 minutes more. Transfer to a wire rack.
5. Reduce oven temperature to 350°F.
6. Meanwhile, prepare filling: Melt butter in a large skillet over medium heat until bubbling. Add 2 tablespoons brown sugar and apple slices. Cook until the apples start to become tender, about 5 minutes. Add cardamom and saffron; remove from heat. Drain the butter from the apples through a fine-mesh sieve into a small bowl and let cool for 10 minutes.
7. Whisk eggs, milk, salt and the remaining ¾ cup brown sugar in a large bowl. Slowly drizzle in the butter, whisking constantly. Whisk in flour until the custard is smooth. Arrange the apple slices in the crust. Pour the custard over the apples. Use a small knife to separate the slices so custard seeps into the crevices.
8. Bake the pie until the custard is set, about 1 hour. Let cool completely on a wire rack, about 2 hours. Cover and refrigerate until chilled, about 1 hour.