1. Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
2. In a large bowl, whisk together the sourdough discard, flour, baking powder, and salt.
3. Add the cold cubed butter and use a pastry cutter or your fingers to mix until the mixture resembles coarse crumbs.
4. Stir in the shredded cheddar cheese and chopped chives.
5. Pour in the milk and mix until just combined; do not overmix.
6. Turn the dough out onto a floured surface and gently knead it a couple of times to bring it together.
7. Pat the dough into a thick rectangle about 1-inch high. Cut out biscuits using a round cutter or glass.
8. Place biscuits on the prepared baking sheet and bake for 15-20 minutes, or until golden brown.