Cover potatoes with water in saucepan, add ½ teaspoon salt and bring to boil. Reduce heat to medium, cover partially and cook until tender all the way through when pierced with a knife, about 30 minutes. Do not drain water, but use a skimmer or a slotted spoon to transfer potatoes from the pot to a bowl.
Bring water back to a boil and add cabbage. Cook uncovered until tender, approximately five to six minutes. Drain.
Heat olive oil over medium heat in a large, heavy nonstick skillet, and add green onions. Cook, stirring until they soften, about three minutes.
Add potatoes to skillet. Smash potatoes to a coarse mash in the pan with a potato masher or back of spoon.
Stir in milk and mix together well until potatoes have absorbed all the milk.
Stir in cabbage and season with ⅛ teaspoon salt (if desireand pepper to taste.
Stir together until heated through and serve.
