Adjust the oven rack to the middle position and preheat the oven to 450°F.
Place the flour, baking powder, salt, and baking soda in a large bowl and whisk to combine.
Using your fingers, a pastry cutter, or a fork, work the shortening into the flour mixture until only pea-sized pieces remain.
Using the slicing side of a box grater, slice the butter into the flour mixture.
Toss the sheets of butter in the flour and then lightly work the butter pieces between your fingers or use a pastry cutter to break them up and coat them with flour.
Place the biscuit mixture into the freezer for 15 minutes.
Add the buttermilk to the chilled flour mixture and stir with a spatula until the dough forms into a ball.
Sprinkle the surface with 2 to 3 tablespoons of bench flour.
With floured hands, pat the dough into a ¼-inch-thick rectangle.
Fold the ends of the rectangle toward the center, one end on top of the other, to create a trifold.
Repeat the process of patting the dough into an 11 x 6 inch ¼-inch-thick rectangle and fold in thirds again for a third time.
Pat the dough to a ½-inch thickness.
Cut out the biscuits using a 3½-inch biscuit cutter dipped in flour.
Place the biscuit rounds 1 inch apart on a parchment-lined baking sheet.
Bake 15 to 17 minutes, rotating the pan once halfway through, until the tops are golden brown.
