Preheat the oven to 450 degrees F. Great an 8 by 8 by 2-inch baking pan well. Sift the flour, baking powder, and sugar into a bowl. Cut in the shortening and butter until the mixture resembles coarse cornmeal. Make a well in the center of the flour and pour in the buttermilk and milk. Mix lightly and quickly with your hands to form a dough moist enough to leave the sides of the bowl. Turn onto a lightly floured surface. Knead by picking up the sides of the dough away from you while pressing down with the palms of your hands and pushing the dough away. Repeat 6 or 7 times. Work the dough into a large ball while kneading. Keep your fingers dry by frequently dipping them in dry flour. Pinch off portions of dough for desired size biscuit. Press lightly to make the biscuits look flat on the pan. Make sure the biscuits touch each other. Bake for 15 minutes.
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