Cranberry Apple Pie

For the crust: In a large bowl, whisk together flour, baking powder, and salt. Add shortening and gradually work into flour with a pastry cutter until it resembles a coarse meal, 2 to 3 minutes. Add vinegar and 4 tablespoons ice water. Toss mixture gently, then add remaining ice water until dough begins to come together. (You may need to add more water 1 tablespoon at a time, until all flour is moistened.) Separate dough in half and form two evenly sized balls. Wrap each in plastic wrap and press down to slightly flatten each (this will make rolling easier later). Transfer to refrigerator if using within 24 hours; otherwise transfer to freezer. When ready to use dough, remove from freezer and thaw 15 to 30 minutes before rolling out one ball as the bottom and crust and slicing the other into a lattice. For the filling: Preheat oven to 350 degrees F. Place bottom crust in your pan and brush with egg white (reserve the rest to brush on top of the pie). Place in the freezer while you prepare the filling. In a saucepan over medium heat, melt butter. Stir in flour to form a paste. Add water, sugars, cinnamon, nutmeg, and allspice and bring to a boil. Reduce temperature and let simmer. Meanwhile, combine apples and cranberries in a large bowl. Add brown sugar mixture to apples and toss to coat. Arrange apple cranberry mixture in a mound in pie dish and cover with a lattice crust. Brush with remaining egg white and sprinkle with course sugar, if desired. Bake until apples are soft and crust is deeply golden, about 1 hour.