Preheat oven at about 350 degrees F (175 degrees C). Grease and flour a 9×13 inch pan.
Stir the flour, 2 tbsp of sugar, and salt in a medium bowl. Cut in the shortening until it resembles coarse crumbs. Add and combine egg yolks and 1/2 cup of milk; stir it into the flour mixture.
Roll the half of the dough on a lightly floured surface out to the size of the prepared pan. Cover the inside of the pan with the dough. Then, spread though with a light coating of egg white. Fill with sliced apples and sprinkle with sugar and cinnamon on top. Roll out the remaining dough and put it on top of the apples. Brush using a light coating of egg white.
In a preheated oven, bake it for 35 to 40 minutes until the crust is golden. Beat the confectioner’s sugar, salt, vanilla, and milk in a small bowl until smooth. Drizzle over the cooled bars, and cut into squares.