Preheat the oven to 400 degrees F.
Whisk together the 12 ounces flour, baking powder, baking soda and kosher salt in a large mixing bowl. Using your fingertips, rub the butter and shortening into the dry goods until the mixture resembles coarse crumbs. Make a well in the middle of this mixture and pour in the buttermilk. Stir with a large spoon until the dough just comes together. Then knead in the bowl until all the flour has been taken up.
Turn the dough out onto a floured surface, then start folding the dough over on itself, gently kneading for 30 seconds, or until the dough is soft and smooth. Press the dough into a 1-inch thick round. Using a 3-inch round cutter, cut out biscuits, being sure to push the cutter straight down through the dough to the work surface before twisting to "punch" out the biscuit. Make your cuts as close together as possible to limit waste.
Place the biscuits on a half sheet pan so they just barely touch. Reroll any scraps and punch out as many biscuits as possible. Use your thumb to create a shallow dimple in the top center of each biscuit and bake until the biscuits are tall and light gold on top, 15 to 20 minutes. Turn the biscuits out into a kitchen towel-lined basket and cool slightly before serving.