Preheat your oven to 425°F (220°C). Line a baking sheet with parchment paper.

In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, and granulated sugar (if using) until well combined.

Add the very cold, cubed butter to the dry ingredients. Using a pastry blender, two forks, or your fingertips, cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces remaining.

Pour in the cold sourdough discard and 1/2 cup of cold milk. Mix gently with a wooden spoon or your hands until just combined. The dough will be shaggy and a bit sticky. Avoid overmixing.

Lightly flour a clean work surface. Turn the dough out onto the floured surface. Gently pat the dough into a rough rectangle. Fold the dough in thirds (like a letter) and then pat it down again. Repeat this folding and patting process 2-3 times. This creates flaky layers. Do not knead aggressively.

Pat or roll the dough to about 3/4 to 1-inch thickness. Using a 2.5 to 3-inch biscuit cutter (or a knife for square biscuits), cut out the biscuits. Dip the cutter in flour between each cut to prevent sticking. Press straight down, do not twist, to ensure a good rise.

Gather the scraps, gently pat them together (minimizing handling), and cut out any remaining biscuits. Arrange the biscuits on the prepared baking sheet, leaving about 1/2 inch between them for soft sides, or touching for taller, softer biscuits.

Bake for 12-18 minutes, or until the tops are golden brown and the biscuits are cooked through. Baking time may vary depending on your oven and biscuit thickness.

Optional: As soon as the biscuits come out of the oven, brush the tops with melted butter for extra flavor and shine.

Serve warm with your favorite breakfast accompaniments like jam, butter, honey, or gravy.