Preheat oven to 425 F. Line a baking sheet with parchment paper or a baking mat.
Whisk the flour, baking powder, salt, and baking soda together in a large mixing bowl. In another bowl, whisk together the cottage cheese and milk.
Scatter the grated butter over the dry ingredients and toss to coat.
Pour the cottage cheese and milk mixture over the dry ingredients and, using a fork, gently toss, turn and stir until you've achieved a soft dough.
Lightly dust a work surface with flour and turn out the dough. Dust the top of the dough with flour and pat the dough out with your hands into a circle until 1/2 inch thick.
Slice dough with a sharp knife into 8 triangle wedges. Transfer them to the baking sheet.
Bake biscuits for 14-18 minutes, or until tall, puffed and golden brown. Remove them from the baking sheet and serve immediately.