Remove any tough outer leaves from the cabbage, then cut it into quarters and remove the core. Thinly slice the cabbage using a sharp knife or a mandoline.

Grate the apple and finely chop the onion. Set aside.

Heat the butter or oil in a large pot over medium heat. Add the chopped onion and sauté until soft and translucent, about 5 minutes.

Stir in the sugar and cook for another minute until the sugar dissolves and begins to caramelize slightly.

Add the sliced cabbage, grated apple, vinegar, and apple juice or water to the pot. Stir well to combine.

Season with cinnamon, cloves, bay leaf, salt, and pepper. Mix thoroughly.

Cover the pot with a lid, reduce the heat to low, and simmer for 40–50 minutes, stirring occasionally. If the mixture seems dry, add a splash of water or apple juice as needed.

Taste and adjust the seasoning, adding more vinegar or sugar to achieve the perfect balance of sweet and sour.

Once the cabbage is tender and the flavors have melded together, remove the bay leaf and cloves (if using whole ones).

Serve warm as a side dish to roast pork, duck, sausages, or schnitzel.