Place potato chunks in a large pot. Add enough cool water to cover by an inch. Bring to a boil over high heat. Add a little salt to the water. Cook 12 minutes, until potatoes are tender, and drain.
Transfer potatoes to a serving dish and mash with a potato masher. Add milk, butter and 1 teaspoon salt; mash until smooth. Stir in green onions and chives and serve.