Place potatoes in a saucepan with enough water to cover. Bring to a boil, and cook for 15 to 20 minutes, until tender.
Place bacon in large, deep skillet. Cover over medium heat until evenly brown. Drain, reserve drippings, crumble and set aside. In the reserved drippings, sauté the cabbage and onion until soft and translucent. Putting a lid on the pan helps the vegetables cook faster.
Drain cooked potatoes, mash with milk and season with salt and pepper. Fold in the bacon, cabbage, and onions, then transfer the mixture to a large bowl serving bowl. Make a well in the center, and pour in the melted butter. Serve immediately.