Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a medium bowl, mix together the flour, 2 tablespoons of sugar, and salt.
Cut in the shortening using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Add the egg yolks and 1/2 cup of milk to the flour mixture and stir until well combined.
Roll out half of the dough on a lightly floured surface to fit the size of the prepared pan. Place it in the pan.
Spread a light coating of egg white over the dough in the pan.
Fill the pan with sliced apples, and then sprinkle the apple filling with 3/4 cup of sugar and the ground cinnamon.
Roll out the remaining dough and place it over the apples, brushing the surface with a light coating of egg white.
Bake in the preheated oven for 35 to 40 minutes, or until the crust is golden brown.
In a small bowl, beat together the confectioners’ sugar, pinch of salt, vanilla extract, and 3 tablespoons of milk until smooth.
Drizzle the icing over the cooled apple pie bars before slicing into squares and serving.