To make the pie crust, stir the flour and salt in a large bowl. Cut in the shortening and butter with a pastry blender or two knives until the mixture resembles coarse crumbs. Sprinkle with the ice water, a tablespoon at a time, and stir with a fork to moisten all the dough. Gather the dough into a ball with your hands. Divide the dough in half. Roll out one half on a lightly floured surface and fit it into a 9-inch pie plate. Roll out the other half on a lightly floured surface and fit it into a 9 inch pie plate. Roll out the other half and set aside.
Preheat oven to 375 degrees.
Peel and core the apples and cut them into thin slices into a large bowl. Combine the sugar, flour, cinnamon, and allspice in a small bowl and toss with the apples. Spoon the filling into the pastry-lined pie plate. Dot with butter.
Position the top crust over the pie and seal the edges. Cut steam vents in the top crust in a design of our choice. Trim and flute the edges.
Beat one egg with a fork, brush it over the crust, and sprinkle lightly with sugar. Cover edges with aluminum foil or a pie crust shield. Bake for 25 minutes; remove the foil. Bake an additional 25-30 minutes until the crust is golden brown and the filling is bubbly.