Combine the flour, baking powder, sugar, salt, and baking soda in a food processor fitted with the blade attachment. Pulse a few times, until well mixed. Add the shortening and pulse until fine crumbs form. Switch to the grating disk attachment. With the machine running, push the frozen butter through the feed tube.

Transfer the mixture to a large bowl and toss to make sure all the butter shreds are coated with the floury crumbs. Add the buttermilk and fold in using a rubber spatula, running the flat of it through the center of the mixture and then around the edge while you rotate the bowl. Keep at it, being as gentle as possible, until the dry ingredients are evenly hoisted.

Mix the flour, baking powder, sugar, salt, and baking soda in a large bowl with an open hand, using your fingers as a whisk. Add the shortening and use your fingertips to pinch it completely into the flour until the mixture resembles coarse crumbs.

Using a box grater, grate the frozen butter on the large holes into the flour. Toss until all the pieces are coated. Add the buttermilk to the flour mixture. Using your hand as a spatula, gently mix until there are no dry bits of flour left. The dough will be sticky.

Lightly coat your work surface with nonstick cooking spray, then flour. (The spray keeps the flour in place.)

Turn the dough out onto the prepared surface and gently pat into a 1/2-inch thick rectangle. Sprinkle the dough with flour, then fold it in thirds like a letter. Repeat the patting, sprinkling, and folding twice, rotating the dough 90 degrees each time. Pat the dough to 3/4-inch thickness. It should no longer be sticky.

Flour a 2-inch-round biscuit cutter and press it straight down into the dough. Transfer the round to the prepared pan, placing the bottom side up. Repeat, cutting the rounds as close together as possible and spacing them 1-inch apart on the pan. Stack the scraps, pat to 3/4-inch thickness, and cut again. Refrigerate the rounds until cold, at least 15 minutes.

Preheat the oven to 450 degrees F. Butter a baking sheet. Or line a sheet pan with parchment.

Bake until the tops are golden brown and crisp, about 16 minutes. Let cool for 5 minutes on the pan before serving hot.