Cook the potatoes in a large pan of boiling salted water for 15-20 minutes. Remove potatoes to a large bowl with a slotted spoon, draining off all excess water.

Mash with a potato masher until smooth. Add the butter and milk and stir well. Add a bit more milk, if needed to make a smooth, creamy consistency. Season to taste with sea salt.

Add shredded cabbage to the potato water and return to a boil. Cook for 1-2 minutes until cabbage is soft. Drain thoroughly, squeezing off excess water. Mix the cabbage and mashed potatoes together, then stir in the scallions, reserving a handful for garnish. Taste and season if needed with more salt. Place in a large bowl or small individual bowls and sprinkle generously with freshly ground pepper. Scatter reserved sliced scallions over top and drizzle with melted butter.