Wash potatoes and place them in a steamer pot, with their skins on, steam for 30 minutes.
When potatoes are done steaming for 30 minutes, peel potatoes using a knife and fork. Discard peels, place inside of potatoes in a large bowl.
Mash potatoes thoroughly to remove all the lumps.
Add 1/2 cup of butter into hot potatoes, in small pieces. Gradually add half and half, stirring continuously.
Season with black pepper. Set aside.
Meanwhile, while potatoes cook, in a large pot filled with unsalted water, boil the shredded cabbage until it turns a slightly darker color.
Once color changes, add 2 tablespoons butter to pot.
Cover with lid and cook for 2 additional minutes. Remove from heat.
Drain cabbage thoroughly, and add it to the potatoes pan.
Chop already cooked ham or bacon into small pieces, and add to the potato pan.
Chop and scallions, and stir it all together gently.
To serve, add to a bowl or plate, and make a small well or indentation in the top of the potato mound, add butter, and sprinkle with parsley.