Preheat oven to 450F and line a baking sheet with parchment paper or a silpat liner.
Puree the cottage cheese and milk together until smooth in a blender or food processor; set aside.
Whisk together the flour, baking powder, salt, and black pepper in a large bowl.
Cut in the butter with a fork or using two butter knives until it looks like coarse meal. Add the scallion and stir in the cottage cheese/milk puree. (The dough should come together, but not be too wet; if the dough is still too crumbly, you can add milk a little at a time until it comes together.)
Shape the dough into a ball, then flatten it into a disk; wrap it in plastic wrap and chill 10 minutes in the freezer.
Turn the dough out onto a lightly floured surface. Roll or press the dough out to a circle about 7 to 8 inches in diameter and 3/4 inch thick. Use a floured 2 1/2 inch round cookie cutter to stamp out the scones, then gather up the dough scraps and repeat as necessary (you should get about 8 to 10 scones).
Transfer the scones to the prepared baking sheet, lightly brush the tops with a little milk, and bake until puffed and light golden brown on top and bottom, about 14 to 16 minutes.