Buttermilk-Cardamom Pie

Crust: In a large bowl, stir together flour, sugar, and salt. Using a pastry blender or your fingers, cut in shortening and butter until mixture resembles coarse meal, with pea- to almond-size pieces of butter and a few larger chunks remaining (work quickly so that butter and shortening remain cold).

In a small bowl, beat egg with 1/3 cup water and vinegar. Pour egg mixture around edges of flour mixture while working it in with a fork, just until dough starts to clump together. Add more water, 1 tablespoon at a time, if needed. Do not overmix. Lightly dust your hands and work surface with flour. Turn dough out onto surface and press it together. Divide dough in half, shape each half into a flat disk, and wrap in plastic. Refrigerate at least 30 minutes and up to 3 days.

Place one disk of dough on a lightly floured surface (reserve remaining disk for another use). If dough is too firm, let stand 5 to 10 minutes before rolling. Dust a rolling pin with flour and roll out dough into a 12-inch round, about 1/8 inch thick. Brush off any excess flour after rolling. Fold dough in half or gently roll it up around rolling pin and lift to place in a 9-inch pie dish. Press dough lightly into bottom and up sides of dish. Using kitchen shears or a paring knife, trim to a 1/2-inch overhang; fold under. Crimp edges as desired. Prick bottom of dough all over with a fork. Cover with plastic. Refrigerate or freeze at least 30 minutes.

Preheat oven to 375 degrees with racks in center and lower third. Line dough with parchment, pressing it into corners and edges; fill with dried beans or rice. Bake on lower rack 10 to 15 minutes. Remove beans or rice and parchment; bake on center rack until golden brown, about 5 minutes more. Transfer to a wire rack and immediately brush very lightly with egg white. Reduce oven temperature to 350 degrees.

Filling: In a large bowl, whisk together sugar, flour, nutmeg, cardamom, and salt. In a small saucepan, heat butter and vanilla seeds over low, stirring occasionally, until butter is melted. Add butter mixture to sugar mixture and stir until thoroughly combined. Add eggs, one at a time, whisking after each addition. Whisk in buttermilk until smooth and well blended.

Pour filling into warm crust. Place pie dish on a rimmed baking sheet; bake on center rack, rotating halfway through, until filling is set around edges but wobbles slightly in center when gently shaken, 50 minutes to 1 hour. Transfer to a wire rack; let cool at least 1 hour before serving.