Prep the veggies: Begin by thinly slicing the red cabbage. Aim for even slices to ensure consistent cooking. Peel, core, and dice the apples into small pieces. Finally, brunoise the white onion by finely dicing it into small cubes.
Layer in the slow cooker: Drizzle the olive oil (if using) in your slow cooker. Add the sliced cabbage as the base layer. Next, evenly distribute the diced apples and brunoised onions on top of the cabbage.
Add the seasoning: Sprinkle the ground allspice over the cabbage, apples, and onions. Pour the apple cider vinegar evenly across the mixture, and sprinkle the Splenda to your desired sweetness.
Stir and cook: Gently stir everything together in the slow cooker to combine the ingredients. Place the lid on the slow cooker and cook:
On LOW for 2-3 hours for a slow, gradual cook.
Season and serve: Once done, taste the cabbage mixture and adjust the seasoning (salt, sweetness, tanginess) as needed. Stir well before serving.