Crust:
Whisk the dry ingredients together in a large mixing bowl. Add the cubed butter and vegetable shortening and mix briefly with a fork to coat the fats with flour. Cut the fats into the dry ingredients with a pastry blender or two dinner knives, working the mixture until the particles have a coarse, mealy texture similar to that of fresh bread crumbs with some larger pea-size pieces.
Drizzle 1 Tbs. of the ice water around the edge of the bowl, letting it trickle into the crumbs. Flick the moistened crumbs toward the center with a table fork, rotating the bowl as you work. Repeat with the remaining 4 Tbs. ice water, 1 Tbs. at a time. As you add the water, the crums should begin to form larger clusters. Once you've added 5 Tbs. water total, take a handful of crumbs and squeeze them gently; they should hold together. If they easily break apart, the mixture needs more water: add the remaining Tbs., one tsp. at a time, checking the consistency after each addition. If the crumbs still fail to hold together, you can add additional water, but do so sparingly.
Gather a handful of the crumbly dough and press it against the side of the bowl to form a small mass, flouring your hand as needed to prevent excessive sticking. Increase the size of this mass by pressing it into more of the crumbly mixture until you've used up about half of the total mixture in the bowl. Make a second mass of dough with the remaining crumbs. If some of the crumbs on the bottom of the bowl need more moistening, add a few drops of water.
Form the two masses of dough into balls, dust them with flour, and flatten them into 4- to 5-inch disks. Pat the disks to release any excess flour. Score the tops lightly with the side of your hand to create a tic-tac-toe pattern. With cupped hands, rotate each disk on the work surface to smooth the edges of the disks. Wrap each in plastic wrap. Chill at least 30 minutes before using.
Filling:
Preheat oven to 425 degrees F (220 degrees C). Melt the butter in a saucepan. Stir in flour to form a paste. Add water, white sugar and brown sugar, and bring to a boil. Reduce temperature and let simmer.
Place the bottom crust in your pan. Fill with apples, mounded slightly. Cover with a lattice work crust. Gently pour the sugar and butter liquid over the crust. Pour slowly so that it does not run off.
Bake 15 minutes in the preheated oven. Reduce the temperature to 350 degrees F (175 degrees C). Continue baking for 35 to 45 minutes, until apples are soft.