For the crust: Whisk together the flours, granulated sugar, cinnamon, salt and nutmeg in a very large bowl until well combined. Using a pastry cutter or your hands, work the butter and shortening into the dry ingredients until it has a coarse sand-like consistency. Combine the water and vinegar in a small bowl, then add that to the mixture and mix until a dough forms.
Divide the dough into two discs, wrap each in plastic wrap and place in the refrigerator for at least 4 hours.
For the filling: Preheat the oven to 400 degrees F. Line a quarter-sheet tray with parchment paper.
Remove the dough from the refrigerator and roll out one disc on a lightly-floured work surface. Lay the dough on the sheet tray, evenly covering the bottom. (Do not cut off the excess dough yet.) Lay the chocolate bars over the top of the dough. Sprinkle mini marshmallows over the chocolate. Roll out the second dough disc and lay that on top of the marshmallows, covering the pie entirely. Cut off excess dough from the top piece and fold the edge of the bottom dough over the edge of the top dough. Press the edges together with a fork or crimp the edges. Brush with the egg wash and poke several holes in the top with a fork. Bake until golden, 45 to 50 minutes. Allow to cool completely.
For the glaze: Whisk together the powdered sugar, cocoa powder, milk and salt in a bowl until it has the consistency of thick glue. Glaze the top of the pie and immediately add sprinkles. Allow the glaze to set, about 15 minutes. Slice and serve.