In a medium bowl, combine the flour and salt.

Add the cubed cold butter and use a pastry blender or fork to cut it into the flour mixture until it resembles coarse crumbs.

In a small bowl, lightly whisk the reserved egg yolk with the 1/3 cup of milk.

Pour the milk and egg yolk mixture into the flour mixture. Gently combine with your hands until a sticky dough forms.

Divide the dough into two equal portions and flatten each into a disk.

Cover each disk with plastic wrap and refrigerate for at least 30 minutes.

Preheat your oven to 350°F (175°C).

Crush the Cinnamon Toast Crunch cereal into fine crumbs.

On a sheet of waxed paper, roll out one chilled dough disk into a rectangle approximately 15.5 x 10.5 inches.

Carefully transfer the rolled dough into a 10x15 inch jelly roll pan or glass baking dish, ensuring it comes up about 1/2 inch on the sides.

Spread the crushed Cinnamon Toast Crunch evenly over the dough base. Then, arrange the sliced apples on top.

In a small bowl, mix the 1 cup of powdered sugar and 1 teaspoon of cinnamon, then sprinkle this mixture over the apples.

Roll out the second chilled dough disk into a 10x15 inch rectangle.

Place this second dough rectangle on top of the apples. Use your fingers or a fork to seal the edges of the top and bottom dough layers.

Whisk the reserved egg white until foamy and brush it evenly over the top layer of dough.

In a small bowl, combine the 1/2 teaspoon of cinnamon and 2 tablespoons of granulated sugar, then sprinkle this mixture over the egg white wash.

Bake in the preheated oven for 45 minutes, or until the crust is lightly golden brown.

Remove from the oven and let the bars cool in the pan for at least 1 hour.

While the bars are cooling, prepare the glaze. Mix the 1 cup of powdered sugar and 2 tablespoons of milk in a small bowl until smooth.

Drizzle the glaze over the cooled bars.

Let the glaze set completely for 1-2 hours before cutting the bars into desired portions.