Steam the potatoes in their skins for 30 minutes. Peel them using a knife and fork. Chop with a knife before mashing. Mash thoroughly to remove all the lumps. Add 1 stick of butter in pieces. Gradually add hot milk, stirring all the time. Season with a few grinds of black pepper.
Boil the cabbage in unsalted water until it turns a darker color. Add 2 tablespoons butter to tenderize it. Cover with lid for 2 minutes. Drain thoroughly before returning it to the pan. Chop into small pieces.
Add cabbage, scallions, and ham to mashed potatoes, stirring them in gently.