In a Dutch oven or deep pot, layer ingredients, bottom to top Potatoes, carrots, cabbage, scallions. Cover the potatoes and carrots with cold water, just enough to cover potatoes and carrots. The other vegetables will steam during cooking to desired tenderness. Add salt to taste.
Bring to a boil, then reduce heat to maintain a gentle simmer. Cook, covered until potatoes are near fork-tender, carrots crispy tender, about 15-20 minutes. Drain and return all ingredients to pot.
Mash the mixture while adding butter and parsley. The potato mixture should be coarsely mashed & thick. Add milk for thinning if desired. Serve hot with sliced corned beef.