Preheat oven to 400 degrees. In a large bowl, whisk together flour, baking powder, sugar, and salt. Using a box grater, grate frozen butter into flour mixture, tossing after each quarter stick of butter to coat butter shards with flour. Toss to combine.
Stir in 1¾ cups of buttermilk and, using large strokes and stirring from the bottom up, stir just enough to combine the mixture into a crumbly mass. If dough does not come together, stir in more buttermilk a tablespoon at a time, just until mixture barely holds together.
Dust a clean work surface with flour. Scrape dough onto floured surface, gather into a ball, and gently knead with the palms of your hands about ten times, just enough to form a cohesive ball. Sprinkle a little more flour onto dough and gently roll or pat to ¾-inch thickness.
Dip a 2½-inch-round biscuit cutter (or glass) in flour and, punching straight down without twisting, cut out the biscuits. Punch rounds as close together as possible for the most first-roll biscuits (re-rolled dough is always chewier).
Place biscuits on a baking sheet. Bake 20 minutes. Let biscuits rest 5 minutes before serving, to allow the steam inside the biscuit to finish cooking the center.