Prepare the vegetables: Core the cabbage and roughly chop it into large bite-size pieces. Thinly slice the onion.
Layer in the slow cooker: Add the cabbage to the bottom of a 4- to 6-quart slow cooker. Scatter the sliced onion over the cabbage.
Add the kielbasa: Arrange the sliced kielbasa on top of the vegetables. This helps the juices from the sausage drip down and flavor the cabbage as it cooks.
Pour in the liquid: Pour the chicken broth evenly over everything in the slow cooker. Gently press down the mixture with a spoon so the cabbage starts to settle.
Cook: Cover and cook on LOW for 5–6 hours or on HIGH for 3–4 hours, until the cabbage is very tender and the kielbasa is heated through and juicy. Stir once about halfway through if you’re home, but it’s not strictly necessary.
Finish and serve: Give everything a good stir so the sausage and cabbage are evenly combined. Taste and add a pinch of salt and pepper if needed. Serve hot, making sure everyone gets a mix of sausage, cabbage, and that flavorful broth.
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