Place potatoes, onion, salt, pepper, butter and milk in a 4 quart pan. Bring slowly to just a boil. Turn heat down a little - you want the soup just at boiling; less than a full boil, more than a simmer. Stir often. this is important, milk scorches easily. Cook until potatoes are done, about 20 minutes or so.
Remove from heat. Using a stick blender, give the soup 3-4 pulses. (The more you pulse, the small the pieces of potato.)