Cut the butter into small cubes and return to the refrigerator until ready to use.

In the bowl of a stand mixer fitted with the paddle attachment, add the flour, baking powder, salt, and sugar. Mix briefly to distribute.

Add the cold butter cubes and mix on low speed until the butter mostly disappears and only a few pea-sized pieces remain, about 10 minutes.

Add all the sourdough discard and mix on low just until incorporated and a dry, shaggy dough forms. Do not overmix.

Scrape the shaggy dough onto a smooth surface. Drizzle the buttermilk over the dough 1 tablespoon at a time and gently massage and squeeze until the dough just holds together. It should not feel wet. Add up to 1 tablespoon more buttermilk if needed.

Working quickly to keep the butter cold, press the dough flat to about 1½ inches thick and fold into thirds like a letter. Repeat this press-and-fold twice more.

Press the dough into a rough square, wrap tightly in plastic wrap, and refrigerate for 30 to 60 minutes.

Preheat the oven to 375°F convection or 400°F conventional. Line a baking sheet with parchment paper.

Unwrap the dough and roll it out on the plastic wrap to approximately a 7-inch square. Trim all four sides with a sharp knife or bench scraper so the square measures approximately 6 inches on each side.

Cut the square into thirds along the top edge, then rotate and cut into thirds again. You will have 9 square biscuits, each about 2 inches wide.

Gather the scraps, press into a 4x2-inch rectangle, and cut in half to make 2 additional biscuits.

Place the biscuits about 1 inch apart on the prepared baking sheet and brush the tops with egg wash.

Bake for 10 to 12 minutes, until the edges are golden brown and the tops offer a little resistance when pressed lightly.