Remove tough outer leaves from the cabbage and cut it into 6–8 wedges, keeping part of the core attached.
Scrub the potatoes and cut them into 1 ½- to 2-inch chunks.
Place the potatoes in an even layer in a 5- to 6-quart slow cooker.
Arrange the cabbage wedges over the potatoes.
Scatter the butter pieces evenly over the cabbage and potatoes.
Cover and cook on LOW for 6 hours and 30 minutes, or on HIGH for 4 hours, until the potatoes are fork-tender and the cabbage is soft.
Do not stir during cooking.
Lift the cabbage out with a wide spatula and spoon the potatoes into bowls.
Drizzle the buttery cooking juices over each serving and serve hot.
