Adjust oven rack to lower-middle position and preheat to 400°F (200°C).
Sift flour into a medium bowl, then add sugar, baking powder, baking soda, and salt; whisk until well combined.
Add butter, toss to break up the pieces, and smash each cube flat. Continue smashing and rubbing until butter has mostly disappeared into a floury mix.
Add yogurt, and stir with a flexible spatula until the flour has been fully absorbed. The dough will seem rather crumbly and dry at first, but keep mixing until it finally comes together.
Once the dough forms a rough ball, turn out onto a lightly floured surface.
With your bare hands, gently pat the dough into a squarish shape about ½ inch thick, then fold in half; repeat twice more for a total of 3 folds.
Finish by patting the dough to a thickness of ¾ inch. Cut into 1 ¾-inch rounds and arrange in a 10-inch cast iron skillet.
Gather scraps into a ball, pat and fold a single time, then cut as many more biscuits as you can.
Bake until the biscuits are well-risen and golden brown, about 20 minutes.
Let the biscuits cool about 5 minutes to help set their crumb, then serve as desired.
