Preheat oven to 375 degrees F.
In processor, place flour, salt, shortening and butter with 1 Tbs of sugar.
Pulse till it looks like cornmeal ( about 6 one second pulses ).
Beat egg yolk in measuring cup with some milk and then add enough milk to make 1/3 cup total liquid.
Stir into flour mixture until all flour is damp. Divide the dough in half. Place 12x12 sheet of plastic wrap on counter and roll half the dough into a rectangle and fit into a 8x8 inch pan.
Combine remaining sugars and spices in one bowl. Peel and slice apple, add to medium bowl and sprinkle a bit of sugar spice mixture after each apple. Sprinkle any remaining sugar/spice after last apple and stir to coat.
Put apple mixture in pan over bottom crust.
Roll out remaining dough and place over apples. Seal edges and cut slits in top dough.
Beat a tsp of egg white with tsp of water till frothy and brush on crust.
Bake in the preheated oven for 50 minutes, or until golden brown.
Combine powdered sugar, cream and vanilla with a pinch of salt to make icing.
Let cool for 10 minutes and brush on icing.