Put the potato pieces in a saucepan and just cover them with water. Put the green onions and cabbage on top of the potatoes.
Bring to a boil, then cover and the lower the heat to a simmer. Cook about 20 minutes, until the potatoes are soft and cabbage are cooked through and soft.
Drain and mash in the butter, milk, salt and pepper.
In a skillet, heat a bit of oil. Drop a large spoonful of the potato and cabbage mixture in the pan and flatten it slightly. Cook until lightly browned on one side, then flip over and cook the other side.