Prepare the Ingredients: Slice the red cabbage and onion, and dice the apples.
Sauté Onions: In a large pot, heat olive oil over medium heat. Add the sliced onions and cook until translucent.
Add Cabbage: Stir in the red cabbage, mixing well with the onions.
Add Apples: Fold in the diced apples, allowing them to mix with the cabbage.
Season: Pour in the apple cider vinegar, and sprinkle with brown sugar, salt, pepper, cinnamon, and nutmeg.
Simmer: Cover the pot and reduce the heat to low. Let it simmer for about 30 minutes, stirring occasionally, until the cabbage is tender.
Serve: Adjust seasoning to taste and serve warm.