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Preheat oven to 450 degrees F.
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In a large mixing bowl, combine flour, baking powder, baking soda, and salt. Using a fork, cut the butter and shortening into the dry ingredients until the mixture looks like crumbs.
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Make a well in the center of the flour mixture and pour in the cold buttermilk. Stir just until the dough comes together. (The dough will be very sticky.)
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Turn the dough out onto a floured surface. Sprinkle the top of the dough generously with flour and gently fold the dough over on itself 5 or 6 times, adding flour as needed.
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Press the dough flat until it is about 1/2-inch thick. Cut out biscuits with a 2-inch circular cutter.
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Place the biscuits on baking sheet about 1-inch apart. Reform scrap dough, working it as little as possible; continue pressing to 1/2-inch thick and cutting more biscuits.
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Bake for 15-20 minutes, or until the biscuits have risen and are golden on top.