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