Preheat oven to 425°F (220°C) and line a rimmed baking sheet with parchment paper or a silicone mat. Place the baking sheet in the refrigerator or freezer while you make the dough.
Cut butter into small cubes and freeze for 10-15 minutes, or freeze a stick and grate it on the large holes of a box grater. Return grated or cubed butter to the freezer until ready to use.
Stir down the sourdough discard to remove large bubbles, then measure out 1/2 cup (120g) of the stirred-down discard and set it aside.
In a large mixing bowl, combine flour, baking powder, baking soda, salt, and sugar. Whisk together for about 30 seconds until evenly mixed.
Add the very cold butter to the flour mixture. Toss quickly with your fingertips until coated and the mixture looks like rough, shaggy crumbs with some pea-sized pieces, about 30-45 seconds. Work quickly to keep the butter cold.
In a small bowl, combine the sourdough discard and cold buttermilk. Stir together briefly until combined.
Pour the wet ingredients into the flour mixture. Use a fork or your hands to stir and fold until a shaggy, rough dough forms. Stop as soon as no dry flour is visible.
Lightly flour a work surface and turn out the dough. Gently press into a rough rectangle about 3/4 inch (2 cm) thick. Fold in thirds like a letter, rotate 90 degrees, and fold again. Press out once more to 3/4 inch thick.
Press a sharp 2.5 to 3-inch (6.5 to 7.5 cm) biscuit cutter straight down into the dough without twisting. Place cut biscuits on the cold lined baking sheet with sides touching. Gather scraps and repeat.
Brush the tops generously with heavy cream or melted butter. Bake at 425°F (220°C) for 13-16 minutes until tops are golden brown and bottoms are lightly browned. Let cool on the pan for 3-5 minutes before serving.