Cut the butter and shortening into cubes and chill. While chilling, combine all other incredients except buttermilk in a food processor, and pulse to combine. Drop in the butter and shortening cubes a few at a time and process until the mixture looks crumby. Pour into a mixing bowl, and make a well in the center. Pour in the buttermilk and fold gently until the batter just comes together. Turn it out onto a floured surface, flatten, and fold over itself very gently about 5 times. Flatten to about 1 inch, and then cut rounds. Bake at 450 until biscuits are tall and golden on top, ~15 minutes.
Note: This is based on Alton Brown's biscuits.