Arrange the sliced smoked sausage over the cabbage in an even layer. The sausage will brown slightly at the edges and its juices will drip down, seasoning the vegetables.
Pour the chicken broth evenly over everything in the slow cooker. The liquid will not completely cover the ingredients; that’s fine. As the cabbage releases its juices, it will create plenty of savory broth.
Cover and cook on LOW for 6 to 8 hours, or on HIGH for 3 to 4 hours, until the potatoes are very tender and the cabbage is soft and translucent. The sausage should be heated through and lightly browned around some of the edges.
Once cooked, gently stir from the bottom to mix the sausage, cabbage, and potatoes together without mashing the potatoes too much. Taste and, if you like, add a pinch of salt and black pepper at the table.
