Sift the all-purpose flour, cornmeal, sugar, baking powder, and salt into a large mixing bowl. Whisk the dry ingredients together to make sure everything is evenly combined.
Grate the very cold butter directly into the flour-cornmeal mixture. Using clean hands, gently cut the butter into the dry ingredients until it is evenly distributed. It’s okay if some small chunks of butter remain.
Create a well in the center of the flour-cornmeal mixture, and pour in half of the cold buttermilk. Use a rubber spatula to gently fold the dry ingredients into the buttermilk until the dough begins to hydrate. Add the remaining buttermilk, and use your hands to gently press the dough together.
Turn the dough out onto a clean, dry, lightly floured work surface. Continue gently bringing the dough together until it is no longer crumbly and can be formed into a ball.
Sprinkle a little flour over the dough, and use a rolling pin to roll it to about 1 inch thick. Fold the dough over itself, turn it 90 degrees, and roll it out again. Repeat this process about 8 times to create layers in the biscuits.
Roll the dough to about 1 ½ inches thick. Using a biscuit cutter or round drinking glass, cut straight down through the dough, then lift the cutter straight back up. Do not twist the cutter to release the biscuit. If using a glass, you may hear a small release of air when the biscuit is cut through.
Gently bring the remaining scraps of dough together, roll them out, fold the dough over itself, and cut additional biscuits. You should get about 10 biscuits total.
Preheat the oven to 425°F. Arrange the biscuits on a nonstick baking sheet, leaving at least 1 inch of space between them. Refrigerate the biscuits for about 15 minutes while the oven preheats.
Bake for 20–25 minutes, or until the biscuits have risen and are golden brown. Serve warm.