To make the crust, combine the flour, salt, and sugar in a large bowl. Add the butter and shortening and toss into the flour to coat. Cut the fat into the flour mixture with a pastry knife until it resembles coarse breadcrumbs.
Add cheese and stir to combine. Slowly drizzle ice water over the flour mixture a few tablespoons at a time and rub mixture together with your fingers, gently squeezing the liquid into the dough. Keep adding more water until the dough holds together but is not sticky.
Gather the dough into a ball, cut in half and wrap each half in plastic wrap. Chill in the refrigerator for at least 20 minutes, or until firm enough to roll out. Dough can be made up to a day in advance.
To make the filling, combine apples, cherries, lemon juice, vanilla, sugar, salt, and flour in a large bowl. Stir until everything is thoroughly mixed.
Heat oven to 425°F and arrange rack in the bottom third. Place a baking sheet covered with foil on the rack to heat with the oven.
Remove one piece of dough from the refrigerator. Place on a lightly floured surface and roll dough into an 11-inch circle, about 1/4-inch thick. Transfer dough to a 9-inch pie pan and press dough into pan. Trim the edges leaving about 1/2-inch of dough overhanging the sides.
Scrape the filling into the crust and dot the top with butter. Roll out the remaining dough to about 1/4-inch thickness and place on top of the filling. Trim the edges even with the bottom crust and press the two together to seal. Crimp the edge in a decorative pattern if you wish and place the pie in the freezer for about 15 minutes.
Whisk together the egg and water. Remove pie from freezer and cut 4 to 5 slits in the top or cut out a decorative pattern. Brush the top with the egg wash and sprinkle with sugar.
Place pie on the heated baking sheet and bake for 20 minutes. Lower temperature to 375°F and bake for another 40-45 minutes or until top is brown and fruit is bubbly. Let sit for at least 1 hour before serving.