Add potatoes to a large pot, cover with water and salt well. Bring pot to a boil and simmer until tender, about 15 minutes.
When potatoes are tender, drain, mash, and set aside in another dish. Return empty pot to heat.
Melt 6 tablespoons butter in the pot, then add the sliced cabbage. Season with salt and pepper, and cook until cabbage is soft and wilted, about 5 minutes.
Add the garlic and white part of the green onions. Stir until fragrant, 1-2 minutes.
Add milk and cook until milk is warm, 2-3 minutes. Add the potatoes and mix until everything is combined and creamy. Season with salt and pepper to taste.
To serve, transfer colcannpon to a serving bowl. Make a well in the center and add a large square of butter, about 2 tablespoons. Garnish with chives and green parts of the green onion. Serve.