Chop: Core and chop the green cabbage into large, bite-sized chunks. Peel the potatoes and cut them into uniform 1-inch cubes so they cook at the same rate.
Layer: In the basin of your slow cooker, combine the chopped cabbage, cubed potatoes, and sliced onion.
Season: Drizzle the olive oil evenly over the vegetables, then sprinkle with the salt and black pepper. Toss gently to distribute the seasoning.
Add Liquid: Pour the vegetable broth over the top of the mixture.
Slow Cook: Cover with the lid and cook on Low for 6–8 hours (or on High for 3–4 hours) until the potatoes are fork-tender and the cabbage is perfectly softened.
Toss & Serve: Give everything a gentle stir right before serving to distribute the remaining savory juices at the bottom of the pot.