Preheat oven to 450 degrees F. Line a baking sheet with parchment paper. Or you can bake them in a cast-iron skillet.
In a large mixing bowl, whisk together flour, baking powder, baking soda, and salt.
Stir in the frozen grated butter, making sure all those flakes of butter are coated in flour.
Add the shredded cheese and chives, toss to combine.
Make a well in the center, add the buttermilk. Stir just until combined.
Turn the dough out onto a well-floured surface. Keep a small pile of extra flour on hand to add to your surface or your hands as needed.
Flour your hands and bring the dough together, then lightly fold it in half in a gentle kneading motion. Do this about 5-6 times until your dough comes together and is beginning to feel smooth. Pat dough out to about 1 1/2 inch thick.
Using a floured cutter, cut the dough into desired sizes. DO NOT twist the cutter. (I use a 3-inch biscuit cutter.) Place the cut biscuits onto the prepared baking sheet, close together but not touching.
Brush tops with a little buttermilk. Or you can also brush them with melted butter after baking.
Bake for about 12-15 minutes,until they have risen nice and tall and are golden brown on top.