1. In a large mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Make sure these are thoroughly combined to ensure even leavening throughout your biscuits.

2. Add the cold, cubed butter to the dry ingredients. Using a pastry blender, two knives, or your fingertips, cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining. This is key for flaky layers.

3. In a separate medium bowl, whisk together the sourdough discard and buttermilk until well combined.

4. Pour the wet ingredient mixture into the dry ingredient mixture. Stir gently with a spoon or spatula until just combined. Be careful not to overmix; the dough will be shaggy and a bit sticky, which is exactly what you want for tender biscuits.

5. Gently fold in the shredded cheddar cheese until it’s evenly distributed throughout the dough.

6. Turn the dough out onto a lightly floured surface. Gently pat the dough into a rectangle about 3/4 to 1 inch thick. Use a 2-inch biscuit cutter or a sharp knife to cut out biscuits. For a classic round shape, press straight down with the cutter and avoid twisting. For square biscuits, simply cut the rectangle into squares.

7. Place the cut biscuits onto a baking sheet lined with parchment paper, leaving about an inch between each. If you prefer softer sides, place them closer together. Bake in a preheated oven at 425 F (220 C) for 15-18 minutes, or until the tops are golden brown and the biscuits are cooked through.

8. Once out of the oven, brush the tops of the hot biscuits with melted butter for an extra touch of richness and shine. Serve immediately.