Cut potatoes up into chunks and boil for 15 to 20 minutes in salted water. Remove potatoes to a bowl with slotted spoon, removing excess water from them. Do not discard water they were boiled in.
Mash potatoes with potato masher until smooth and add the butter and milk.
Stir well.
Add more milk, as needed, for a smooth and creamy consistency. Salt to taste.
Add shredded cabbage to the potato water and boil for 2 to 3 minutes until soft. Drain thoroughly through colander or strainer, squeezing out any excess water. Mix cabbage into potatoes and then stir in the green onions after retaining a small handful to use as a garnish.
Salt and pepper to taste. Garnish with scattered onions and a drizzle of melted butter.