Toss the potatoes, butter, 1 tablespoon salt and ½ teaspoon pepper together in a 6-quart slow cooker. Add 1 cup of water, then cover and cook on high until the potatoes are tender, about 4 hours. (The potatoes might have browned lightly in spots but that is okay.)
Remove the lid and add the sour cream and 1 ½ cups warm milk to the potatoes. Use a potato masher to smash the potatoes until they are mostly smooth. If the potatoes need to be thinned out, stir in the remaining ½ cup warm milk. Season to taste with additional salt and pepper. Garnish with chives.
