1. Preheat your oven to 400 F (200 C). Line a large baking sheet with parchment paper or a silicone baking mat to prevent sticking and make cleanup easier.

2. In a large mixing bowl, whisk together the all-purpose flour, baking powder, salt, and baking soda until well combined. This ensures even distribution of the leavening agents.

3. 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 remaining. The cold butter is key for flaky biscuits.

4. Add the shredded cheddar cheese to the flour and butter mixture, tossing to combine. Then, pour in the sourdough discard. Mix gently with a spoon or spatula until just combined. The mixture will be shaggy and somewhat dry.

5. Gradually add the cold milk, stirring just until the dough comes together. Be careful not to overmix, as this can lead to tough biscuits. The dough should be sticky and soft, not smooth.

6. Using a large spoon or an ice cream scoop, drop generous spoonfuls of dough onto the prepared baking sheet, leaving about 2 inches between each biscuit. You should get about 10-12 biscuits.

7. Place the baking sheet in the preheated oven and bake for 15-20 minutes, or until the biscuits are puffed up, golden brown on top, and cooked through. If desired, you can brush the tops with a little extra milk before baking for a slightly glossier finish.

8. Remove the biscuits from the oven and let them cool on the baking sheet for a few minutes before transferring them to a wire rack. Serve warm for the best flavor and texture.