In a large bowl, combine the sliced apples, sugar, flour, and cinnamon. Toss until all the apple slices are evenly coated. Set aside while you prepare the crust—this gives the apples time to release some of their juices.

In another mixing bowl, whisk together the flour, salt, and sugar. Cut in the shortening with a pastry cutter or fork until the mixture resembles coarse crumbs. In a measuring cup, combine the two egg yolks and add enough water to reach 1 cup. Stir this into the flour mixture until a dough forms. Divide the dough in half.

Roll one half of the dough into a rectangle large enough to fit a 10x15-inch jelly roll pan with sides. Carefully lay it into the pan, pressing it evenly across the bottom and slightly up the edges.

Spread the apple mixture evenly over the crust, making sure the apples are distributed well from corner to corner.

Roll out the second half of the dough into a rectangle and place it over the apple filling. Pinch or crimp the edges to seal. Brush the top with the reserved egg white for a golden finish. Use a sharp knife to cut a few slits in the top crust to allow steam to escape while baking.

Bake at 350°F (175°C) for 45–60 minutes, or until the crust is golden brown and the filling is bubbly.

While the strudel bakes, mix powdered sugar, vanilla extract, and just enough milk or cream to make a thin glaze.

Spread the icing over the hot crust right after removing it from the oven. The glaze will soak slightly into the crust, adding sweetness and shine. Let cool before slicing into squares or bars.