Step 1Heat oil and butter in 5-quart Dutch oven over medium heat. Add onion and garlic and cook, stirring occasionally, until onion is tender, about 5 minutes.
Step 2Stir in shredded cabbage, water, vinegar, sugar, caraway seeds and salt. Bury apple quarters and bacon pieces in cabbage. Bring to boil, then reduce heat and simmer, covered, until very tender, about 2 hours. Check cabbage periodically during simmering and stir. If cabbage looks dry, add a bit more water.
Step 3Adjust seasoning. Cool thoroughly, then refrigerate overnight. Reheat over low heat before serving.