Preheat oven to 375°F (190°C).

In a large bowl, combine flour and salt. Cut in shortening until mixture resembles coarse crumbs.

Beat egg yolk in a measuring cup and add milk to make 2/3 cup of total liquid. Stir into flour mixture until all flour is damp. Divide the dough in half.

On a floured surface, roll half the dough into a rectangle and fit it into a 9x13-inch pan.

In a large bowl, combine apples, brown sugar, white sugar, cinnamon, and nutmeg. Mix well and put the apple mixture in the pan over the crust.

Roll out the remaining dough and place it over the apple mixture. Seal the edges and cut slits in the top crust.

Beat the egg white until frothy and brush it on the top crust.