Make the Apple Filling: In a large bowl, combine the sliced apples, sugar, all-purpose flour, and cinnamon. Toss everything together until all the apple slices are evenly coated. Set this bowl aside while you prepare the crust—this mandatory resting period gives the apples time to release some of their natural juices.

Prepare the Crust: In another large mixing bowl, whisk together the flour, salt, and sugar. Cut in the shortening with a pastry cutter or a heavy fork until the mixture resembles coarse, pea-sized crumbs. In a measuring cup, combine the two egg yolks and add enough cold water to reach exactly the 1-cup line. Stir this wet mixture into the flour mixture until a soft dough forms. Divide the dough evenly in half.

Roll the Bottom Crust: Roll one half of the dough into a large rectangle, making it big enough to fit a 10×15-inch jelly roll pan with sides. Carefully lay the dough into the ungreased pan, pressing it evenly across the bottom and slightly up the edges to form a border.

Add the Filling: Spread the resting apple mixture evenly over the bottom crust, making sure the apples are distributed well from corner to corner.

Add the Top Crust: Roll out the second half of the dough into a similar-sized rectangle and carefully place it over the apple filling. Pinch or crimp the edges of the top and bottom dough together to seal the pastry. Brush the entire top crust with the reserved egg white for a beautiful golden finish. Use a sharp knife to cut a few small slits in the top crust to allow trapped steam to escape while baking.

Bake the Strudel: Bake in a preheated oven at 350°F (175°C) for 45–60 minutes, or until the crust is a deep golden brown and the fruit filling is visibly bubbly through the vents.

Make the Icing: While the strudel is in its final minutes of baking, whisk together the powdered sugar, vanilla extract, and just enough milk or cream to make a thin, pourable glaze.

Glaze and Cool: Spread or drizzle the icing evenly over the hot crust right after removing the pan from the oven. The hot glaze will soak slightly into the flaky crust, adding incredible sweetness and shine. Let the entire pan cool completely on a wire rack before slicing it into squares or bars!