Preheat the oven to 425°F (220°C) with a rack in the middle and line a baking sheet with parchment. Cube the butter and freeze it for 10 minutes.

Whisk the flour, baking powder, baking soda, sugar and salt together in a large bowl until evenly combined.

Cut the cold butter into the flour with a pastry cutter or your fingertips until the pieces are pea-sized, with some larger flat flakes. Work quickly so the butter stays cold.

Stir the discard and milk together, add to the flour mixture, and fold until a shaggy dough forms. Add a tablespoon of cold milk only if dry patches remain.

Turn out onto a floured surface and pat into a 1-inch-thick rectangle, roughly 6 by 8 inches. Fold into thirds like a letter, turn a quarter turn, and repeat 3 to 4 times.

Pat to 1 inch thick and cut straight down, without twisting, into 8 biscuits. Place them just touching on the sheet, brush with milk, and bake at 425°F (220°C) for 14 to 17 minutes until tall and deep golden brown. Cool on the pan for 5 minutes before serving.