Melt the butter in a large pot over medium heat.
Add the sliced onion and cook until soft and translucent, about 5 minutes.
Add the shredded cabbage, sliced apples, brown sugar, apple cider vinegar, salt, black pepper, and caraway seeds. Stir to combine.
Cover the pot, reduce heat to low, and let simmer for about 1 hour, stirring occasionally, until the cabbage is tender and the flavors have melded together.
Adjust seasoning with more salt or vinegar to taste, if needed.
Serve warm as a side dish.