To prepare crust: Combine whole-wheat flour, all-purpose flour and salt in a food processor and pulse to mix. Pulse in butter until the mixture resembles coarse meal. Pulse in sour cream and oil. With the motor running, add ice water and process just until the dough comes together. (Add more water, a teaspoon at a time, if necessary.) Divide the dough in half, shape into 2 disks, wrap in plastic and refrigerate while you prepare the filling.

To prepare filling: Clean the food processor and fit with the shredding disc. Cut potato, carrots (or parsnips) and onion into pieces that will fit through the tube. With motor running, drop in the vegetables until they're all shredded.

Combine beef, pork, milk and the shredded vegetables in a high-sided skillet or Dutch oven. Cook over medium heat, mashing and stirring with a potato masher, until the meat is dry and all the liquid has evaporated (the masher helps you check for liquid), 40 to 50 minutes. If the bottom starts to brown or stick before the liquid has evaporated, reduce the heat and continue cooking and mashing until the liquid is gone. Stir in cranberries, allspice, salt and pepper.

Preheat oven to 375 degrees F.

Roll one piece of dough on a lightly floured surface into a 12-inch circle. Transfer the dough to a 9-inch deep-dish pie pan. Scrape the filling into the crust and pat down gently. Roll the remaining dough into a 12-inch circle and cover the filling with it. Trim the crust so it overhangs evenly. Tuck the top crust under the bottom crust, sealing the two together and making a plump edge. Flute the edge with your fingers or crimp with a fork. Brush the top of the crust with egg white.

Bake the pie until the crust is golden, about 45 minutes. Let cool for 20 minutes before cutting.