Melt the butter in a thick-bottomed pan. Sauté the finely chopped onions until tender, then add the finely chopped apple, add the finely chopped garlic and cook for 2 minutes.
Add shredded cabbage to the pan, pour in water, vinegar, cover and simmer for 30 minutes.
Stir the cabbage periodically. At the end, salt and pepper to taste.