Make the crust: Combine the flour and salt in a large bowl. Add the butter and shortening. Using a pastry cutter, gradually work the butter and shortening into the flour until the mixture resembles tiny pebbles. This step should take 3 to 4 minutes.
Lightly beat the egg with a fork, then add it to the crust mixture. Next, add the cold water and vinegar. Stir the mixture together until it?s just combined. Divide the dough in half and form into disks. Wrap in plastic wrap and freeze until firm, about 1 hour.
Make the filling: In a large bowl, toss the apples, cranberries, brown sugar, granulated sugar, flour, salt and lemon juice. Set aside and see how long you can keep from sneaking a slice of apple.
Line 2 baking sheets with parchment paper. With a rolling pin, begin rolling out the dough disks into 12-inch rounds on a lightly floured surface, rolling from the center outward. Be gentle and patient; it?ll take a little time to get the dough completely rolled out. If you think the bottom is really sticking to the surface below, use a nice sharp spatula to loosen the dough and sprinkle some extra flour on top. Then flip it over to finish rolling. Loosen the dough with a spatula, lift and carefully place each round on a prepared baking sheet.
Preheat the oven to 375 degrees F. Place half the apple-cranberry mixture on 1 dough round and the other half on the other round. Fold in the edges so that the dough covers 2 to 3 inches of the apple-cranberry mixture. No need to be artistic?the more rustic, the better. Freeze the pies 30 minutes.
Dot the tops of the pies with the butter chunks. Brush the crust edges with the egg wash. Bake the pies until the filling is golden and bubbling, 35 to 45 minutes. If the crust appears to brown too quickly, cover the edges with foil for the remaining baking time. Let the pies cool slightly, then slice into wedges.