Sift together the flour, salt, baking powder, and baking soda. Cut in the shortening using a pastry blender or your hands or a stand mixer fixed with a dough hook until the mixture resembles coarse crumbs. Make a well in the center and add 1 cup buttermilk. Using your hands, quickly fold the dry ingredients into the buttermilk until a sticky dough forms. You may need to add more buttermilk.
Turn the dough out onto a floured surface. Gently fold the dough over itself 3 or 4 times to create layers. Press the dough out to 1 1/2-inches thick and cut with a floured 3-inch biscuit cutter. Lay the biscuits on an ungreased cookie sheet and brush the tops with buttermilk. Bake for 20 to 25 minutes until risen and golden brown.