In a large bowl, whisk together the flour, baking powder, and salt. Add the chunks of shortening and use a pastry cutter to mix until it looks like coarse meal, about 2 to 3 minutes.

Stir in the white vinegar and 4 tablespoons of ice water. Mix gently, then add the remaining ice water until the dough starts to come together. If necessary, add more water a tablespoon at a time until all the flour is moistened.

Divide the dough in half and form each half into a ball. Wrap these in plastic wrap and slightly flatten them. Put them in the fridge for up to 24 hours or in the freezer for longer storage.

Preheat the oven to 350°F (175°C).

Roll out one ball of dough and place it in your pie pan. Brush the crust with egg white and then place it in the freezer while you prepare the filling.

In a saucepan over medium heat, melt the butter. Stir in 3 tablespoons of flour until it forms a paste. Add the water, white sugar, brown sugar, cinnamon, nutmeg, and allspice. Bring this mixture to a boil, then reduce the heat and let it simmer.

In a large bowl, combine the sliced apples and cranberries. Pour the brown sugar mixture over the fruits and toss everything to coat well.

Remove the pie crust from the freezer and fill it with the apple-cranberry mixture, arranging it into a mound. Roll out the second ball of dough and cut it into strips to create a lattice crust. Place the lattice on top of the filling.

Brush the lattice crust with the remaining egg white and sprinkle with coarse sugar, if using.

Place the pie in the oven and bake for about 1 hour, or until the crust is golden and the apples are tender.

Cut into generous slices and serve it warm with a scoop of vanilla ice cream or a dollop of whipped cream.

For a festive touch, sprinkle a bit of cinnamon on top before serving.