Prepare the Ingredients: Begin by slicing the red cabbage, apples, and red onion into thin strips or slices. Set aside.
Heat the Oil: In a large pot or Dutch oven, heat the olive oil over medium heat.
Sauté the Onions: Add the sliced onions to the pot and sauté until they become translucent, about 3-4 minutes.
Add Cabbage and Apples: Stir in the red cabbage and apple slices, mixing well with the onions.
Season: Sprinkle the sea salt, black pepper, cinnamon, and nutmeg over the cabbage mixture, stirring to distribute the spices evenly.
Deglaze: Pour in the apple cider vinegar and optional red wine, scraping up any browned bits from the bottom of the pot.
Simmer: Add the vegetable broth or water, and bring the mixture to a simmer.
Sweeten: Stir in the erythritol or chosen sweetener.
Cover and Cook: Reduce the heat to low, cover the pot, and let the cabbage braise for about 1 hour, stirring occasionally, until it is tender and the flavors have melded.
Adjust Seasoning: Taste and adjust the seasoning if necessary. Serve warm as a perfect keto-friendly side dish.