2 1/2 cups all-purpose flour
1 tablespoon baking powder
1/2 teaspoon baking soda
1 teaspoon salt
2 tablespoons vegetable shortening, cut into 1/2-inch chunks (ironically, we didn't have veggie shortening, but lard instead. Which works perfectly well, as long as you aren't, you know, vegetarian)
8 tablespoons unsalted butter (1 stick), chilled, lightly floured, and cut into 1/8-inch-thick slices
2 tablespoons unsalted butter, melted and cooled
1 1/8-1/4 cups buttermilk, chilled
Adjust oven rack to lower-middle position and heat oven to 450 degrees. Whisk flour, baking powder, baking soda, and salt in large bowl.
Add shortening/lard to flour mixture; break up chunks with your fingertips until only small, pea-size pieces remain. Working with few butter slices at a time, drop butter slices into flour mixture and toss to coat. Pick up each slice of butter and press between well-floured fingertips into flat, nickel-size pieces. Repeat until all butter slices are incorporated then toss to combine. Freeze mixture in bowl until chilled, about 15 minutes, or refrigerate for about 30 minutes.
Sprinkle 1/3 cup flour across counter, then gently spread flour across area with your palm to form thin, even coating. Add 1 cup plus 2 tablespoons buttermilk to flour mixture. Stir briskly with fork until ball forms and no dry bits of flour are visible, adding remaining 2 tablespoons buttermilk as needed (dough will be sticky and shaggy, but should clear sides of bowl).
With rubber spatula, transfer dough onto center of prepared counter, dust surface lightly with flour, and with floured hands, bring dough together into cohesive ball.
Pat dough into approximate 10-inch square, then roll into 18 by 14-inch rectangle about 1/4-inch thick, dusting dough and rolling pin with flour as needed. Use bench scraper or thin spatula to fold dough into thirds, brushing any excess flour from surface of dough.
Life short end of dough and fold into thirds again to form approximate 6 by 4-inch rectangle. Rotate dough 90 degrees, dusting counter underneath with flour, then roll and fold dough again, dusting with flour as needed.
Roll dough into 10-inch square about 1/2-inch thick. Flip dough over and cut 9-12 rounds with floured biscuit cutter, dipping cutter back into flour after each cut. Carefully invert and transfer rounds to parchment-covered baking sheet, spacing them 1 inch apart.
Gather dough scraps into a ball and roll and fold once or twice until scraps form smooth dough. Roll dough into 1/2-inch thick round and cut more rounds and transfer to sheet.
Brush biscuits tops with melted butter. Bake, without opening oven door, until tops are golden brown and crispy, 15-17 minutes.
Let cool on sheet for 5-10 minutes before serving.