Dissolve the yeast in the warm water in a small bowl and set aside.
Fork-sift or whisk 5 cups of the self-rising flour, baking soda and salt in a stand mixer. Break the shortening and butter into pieces and scatter over the flour. Pulse mixer until the mixture looks like well-crumbled feta cheese.
Make a deep hollow in the center of the flour with the back of your hand. Stir the yeast mixture into the buttermilk and pour this mixture into the hollow. Pulse and add flour as needed to make a very damp, shaggy dough.
Add flour as necessary to make a supple dough. Knead with mixer until dough comes together for about 5 minutes. There are three options at this point: 1) shape now 2) for an even lighter biscuit, move to an oiled plastic bag and let rise until doubled, then punch down and proceed to shape, or 3) refrigerate up to one week and use as desired.
When ready to use, divide dough in half and shape easily. Roll dough out into a 1/3 to 1/2 inch thick round. Fold in half and roll or pat out again until 2/3 to 1 inch thick. Repeat with second half as desired.
For each biscuit, dip a 2 inch biscuit cutter into the reserved flour and cut out the biscuits, starting at the outside edge and cutting very close together, being careful not to twist the cutter. Move the biscuits to a greased baking sheet. Let double at room temperature, about 30 minutes.
Preheat oven to 400 degrees F. Bake the biscuits on the middle rack of the oven. After 6 minutes, rotate the pan in the oven so that the front of the pan is now turned to the back, and check to see if the bottoms are browning too quickly. If so, slide another baking pan underneath to add insulation and retard browning. Continue baking another 6 to 9 minutes as needed, until a light golden brown. When the biscuits are done, remove them from the oven and lightly brush the tops with butter. Turn the biscuits out upside down on a plate to cool slightly. If an angel-like touch is desired, sprinkle with flour.) Serve hot, right side up.
To make angel wings, cut folded biscuits into 2-1/2 inch circles. Cut in half, brush with milk along the curved side of both halves, move to a greased baking sheet with the two curved, moistened sides touching, and bake as directed in the recipe.
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