In a deep bowl, work the butter and shortening into the flour and salt with your hands until you see marble-sized lumps form. Think mixed nuts, but no bigger than almonds. Add ice water a little at a time, sort of "fluffing" the flour. Keep your movements light, as if you are tossing dressing into a salad with your hands. When the dough feels moistened enough, do a "squeeze test" and when it holds together you’re done. Do not overwork the dough! It takes very little time and you’ll be tempted to keep touching it, but don’t! Now divide the dough in half, form each half into a disk shape and roll flat and thin to fit your pie dish. Sprinkle flour under and on top of your dough, and keep rolling surface and pin free from gunk to keep dough from sticking. Trim excess crust to about 1 inch from the dish edge with a scissors., Slice half of the apples directly into the pie, arranging to remove extra space between slices. Cover with half of your other ingredients (sugar, flour, cinnamon, salt), then slice the remaining apples and cover with second half of ingredients. Add dollop of butter on top, cover with top crust, seal and crimp edges, then brush with beaten egg (this gives the pie a nice golden brown shine; be careful not to let egg pool in crevices.) Use a knife to poke vent holes in the top (get creative here with a pattern), then bake at 425 degrees for 15-20 minutes. Turn oven down to 375 degrees and bake for another 30-40 minutes until juice bubbles. Keep an eye on it as it bakes. If it gets too brown, turn down the temperature. To be sure it's done, poke with a knife to make sure apples have softened. Do not overbake or apples will turn mushy.