These savory biscuits can be served at breakfast, lunch, and dinner.
Heat oven to 425 degrees. In a large bowl, whisk together the flour, baking powder, baking soda, and salt. Using your hands or a pastry cutter, cut in butter with the dry ingredients until the mixture is coarse and crumbly. Then cut in the shortening, and mix in the scallions, parsley, and grated cheddar cheese.
Make a well in the center of the flour mixture, pour in buttermilk, and stir with a fork just until dough comes together. Do not overmix. Turn dough onto a lightly floured surface, and knead gently 6 to 8 times.
On a clean work surface, pat dough into a 1-inch-thick round. Cut out biscuits using a floured 3-inch-round biscuit cutter. Do not twist cutter. Gently re-form scraps of dough, and cut out more biscuits.
Transfer the biscuits to a lightly buttered or parchment-lined baking sheet, and bake until golden brown, 12 to 15 minutes, rotating baking sheet halfway through. Serve hot.