Puree half of the cottage cheese in a blender; set aside. Cover potatoes with water by 1 inch in a medium saucepan. Add a large pinch of salt. Bring to a boil. Reduce to a simmer, and cook until tender, about 15 minutes. Drain.
Transfer potatoes to a large bowl. Add both pureed and whole-curd cottage cheese, pepper, chives, butter, and milk. Season with salt. Mash to desired consistency. Serve garnished with chives.