Set a rack in the center of the oven and preheat oven to 450 degrees F. Line a baking sheet with two layers of parchment paper.
In a large bowl, whisk together the flour, cornmeal, baking powder, baking soda, sugar, and salt. Rub 2 tablespoons of the butter into the flour mixture with your fingertips, until it is completely incorporated. Work the remaining butter into the flour until it's in even, pea-sizes pieces. Gently stir in the buttermilk to make a loose dough.
Turn the dough out onto a lightly floured work surface. Pat the dough into a 1/2-inch-thick rectangle. Fold the dough in thirds like a business letter. Pat the dough into a 5 by 8-inch rectangle about 3/4 inch thick. Use a 2- to 3-inch round cutter to make 6 biscuits, and put biscuits on the prepared baking sheet. Press together the scraps of dough, cut 2 more biscuits, and place them on the baking sheet.
Bake until the tops are lightly browned, about 15 minutes. Cool slightly on a rack before serving.