Place the potatoes, cabbage, and green onions into a large sauce pan, fill with water, and bring to a boil. Reduce heat, cover, and simmer until the potatoes are tender, about 20 minutes.
Drain the vegetables and place into a large bowl. Mash the potatoes and vegetables with the butter using a fork until the mixture is chunky, pouring in half-and-half gradually as you mash. Season with salt and pepper, and serve.
