To prepare crust: Mix whole-wheat flour, all-purpose flour, 1 tablespoon sugar and 1/4 teaspoon salt in a medium bowl. Using a pastry cutter or two forks, cut in butter until the pieces are roughly the size of peas. Stir in oil and vinegar with a fork, then stir in just enough water so the dough gathers into a ball.

Dust a large piece of wax paper with flour, then turn the dough out onto it. Dust a rolling pin with flour and roll the dough into a 14-inch circle. Invert into a 9-inch pie pan, gently pressing the dough into the bottom of the pan. Trim any uneven edges, leaving 1/2 inch of dough hanging over the rim. Fold the edges under and crimp into a decorative design. Cover with plastic wrap; refrigerate for at least 30 minutes.

Preheat oven to 350 degrees F.

Prick the crust with a fork several times; line with parchment paper and add enough pie weights or dried beans to cover the bottom. Set the pie pan on a baking sheet. Bake until the crust is firm but not colored, about 20 minutes.

Meanwhile, to prepare filling & bake pie: Whisk squash, evaporated milk, honey, egg yolks and egg in a large bowl until smooth. Stir in 1/3 cup sugar, cinnamon, nutmeg and 1/4 teaspoon salt. Pour the filling into the crust (it will be very full). Place the pie pan on the baking sheet.

Bake the pie until the crust edges are nicely browned, about 40 minutes. Cover the edges with foil and continue to bake until a knife inserted into the center comes out clean, 25 to 40 minutes more. Cool the pie on a wire rack before slicing, at least 2 hours.

Ingredient Notes: Milled from soft wheat, whole-wheat pastry flour contains less gluten than regular whole-wheat flour. It helps ensure a tender result in baked goods while providing the nutritional benefits of whole grains. It is available in natural-foods stores and large supermarkets. Store it in an airtight container in the refrigerator or freezer.

Almond oil is an unrefined oil pressed from almonds. You can find it in many supermarkets and health-food stores. Store it in the refrigerator.

MAKE AHEAD TIP: Prepare crust through Step 2; wrap in plastic wrap and refrigerate for up to 2 days or freeze for up to 2 months (do not thaw before baking).