Prep the produce: core and thinly slice the cabbage, chop the onion, and peel and dice the apples.
Melt the butter in a large Dutch oven over medium heat.
Sauté the onion until soft and translucent, about 4 to 5 minutes.
Stir in the brown sugar and cook 1 minute to lightly caramelize.
Add the cabbage and apples, tossing to coat with the butter and sugar.
Season with salt, pepper, cloves, and caraway, stirring to distribute the spices.
Pour in the apple cider and vinegar and bring to a gentle simmer.
Cover and cook over low heat, stirring every 10 minutes, until the cabbage is tender, 40 to 45 minutes.
Uncover and simmer 5 to 10 minutes to reduce excess liquid. Taste and adjust salt or vinegar, then serve warm.