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Prepare the vegetables: Remove any tough or damaged outer leaves from the cabbage. Cut the cabbage into 6–8 thick wedges, keeping the core attached so the wedges hold together. Scrub the potatoes well (peel if you prefer) and cut them into large chunks, about 1 1/2 inches. Peel the onion and slice it into thick rings or half-moons.
Layer the slow cooker: Place the potato chunks in an even layer on the bottom of a 5- to 7-quart slow cooker. Scatter the sliced onion over the potatoes. Arrange the cabbage wedges on top, nestling them in so they fit snugly but stay mostly intact.
Season and add butter: Sprinkle the salt and pepper evenly over the vegetables. Dot the top with the butter pieces, tucking some down between the cabbage wedges and potatoes so it melts throughout the dish.
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Add the water: Pour the water gently around the edges of the slow cooker so you don’t wash off all the seasoning. The liquid should come about one-third to halfway up the vegetables; they will release additional juices as they cook, creating a rich, savory broth.
Slow cook until tender: Cover the slow cooker with the lid and cook on LOW for 6 to 7 hours, or on HIGH for 3 1/2 to 4 hours, until the potatoes are very tender when pierced with a fork and the cabbage wedges are soft and silky but still hold their shape.
Adjust seasoning and serve: Taste the broth and vegetables, then adjust with additional salt and pepper if needed. Use a large spoon to carefully lift out the cabbage wedges and potatoes, spooning some of the hot buttery broth over each serving. Serve straight from the slow cooker, keeping it on the WARM setting if people will be helping themselves over time.