Line two baking sheets with the dull side of aluminum foil facing up. Set aside. In the bowl of a food processor, pulse to combine flour and salt. Add butter and shortening, and pulse until the mixture resembles fine meal. With the machine running, pour in milk and ice water through the feed tube. Mix until most of the dough has formed a ball, then continue to process for 2 minutes.
Heat oven to 300 degrees, with a rack in the center. Transfer the dough to a lightly floured surface. The dough will appear wet and slick. Sprinkle top of dough lightly with flour. Use a rolling pin to beat across the top of the dough, beating in the flour, until the dough is about 10 inches long and 1/2 inch thick in size. Fold up the dough loosely into thirds, sprinkle again with flour, and beat flour in. Stretch out the dough again until it is about 1/4 inch thick. Sprinkle the dough again with flour, and repeat process for about 10 minutes. The dough will become very smooth, and little bubbles will form in it. As the dough is beaten with the flour and folded, very thin layers form in the dough.
When the dough is smooth and satiny, roll out until about 3/8 inch thick. Cut out biscuit rounds with a 1 1/2-inch biscuit cutter. Transfer the rounds to prepared baking sheets, placing them about 1 inch apart. Prick each round twice with the tines of a small fork, poking fork all the way down through the dough to the baking sheet.
One sheet at a time, bake the biscuits 15 minutes; reduce heat to 200 degrees. Continue to bake until biscuits are golden brown on the bottom but not colored on the top; biscuits will dry out in center as well. Watch carefully, this can take anywhere from 15 to 30 minutes more. The biscuits actually turn a very slight white-pink color when done; they should not be golden or brown on top at all. Continue to sprinkle any remaining dough with flour, and beat and bake any scraps of dough until all the dough has been used. Biscuits freeze well in an airtight container, up to 1 month.