01 - Melt butter or heat oil in a large heavy-bottomed pot over medium heat.
02 - Add chopped onion and sauté until softened, about 3 minutes.
03 - Stir in diced apple and cook for 2 more minutes.
04 - Add sliced cabbage to the pot, tossing to coat with fat.
05 - Sprinkle salt, black pepper, and brown sugar over the cabbage; stir thoroughly.
06 - Add cinnamon stick, cloves, allspice, and bay leaf to the mixture.
07 - Pour in apple cider vinegar and water; stir to combine.
08 - Bring to a simmer, cover, reduce heat to low, and cook 50 to 60 minutes, stirring occasionally, until cabbage is tender and flavors develop.
09 - Remove the lid for the last 10 minutes if a thicker consistency is preferred.
10 - Discard cinnamon stick, cloves, allspice, and bay leaf before serving; adjust seasoning as needed.