Preheat oven to 450 degrees F. In a large mixing bowl, whisk together flour, baking powder, baking soda and salt. Using a pastry blender or your finger tips, quickly cut shortening into flour mixture until combined. After you've cut in the shortening, cut cold butter into the flour mixture until you have various sizes no larger than peas. (See picture within post to see how this should look.) This should also take less than a minute. You want your butter to stay cold so work quickly. Make a well in the center of the flour and pour in the buttermilk. Working from the outside in, bring the flour into the center with a large spoon, scooping and turning bowl until the buttermilk is incorporated into the flour. Use a light hand here. We're not vigorously stirring, but simply gently tossing the flour together with the buttermilk until it's combined. Turn the wet sticky dough out onto a well floured surface. Keep a small pile of extra flour on hand to add to your surface or your hands as needed. You'll see in the video that I'm pretty liberal about using the flour in this step. Flour your hands and bring dough together, then lightly fold it in half in a gentle kneading motion. Do this about 10-11 times until your dough comes together and is beginning to feel smooth. Pat dough into a rectangle or square just under an inch thick. Using a floured knife or something long enough to make one cut across the dough, cut the dough into desired sizes. I usually make big biscuits and cut mine into 9 pieces. Turn biscuits upside down and place onto an ungreased baking sheet, close together but not touching. Brush tops with a little bit of buttermilk and bake until they have risen nice and tall and are golden brown on top, about 15 minutes. Serve warm.