Remove the outer leaves from the head of cabbage, remove the core, and dice the cabbage. Place in a heavy bottomed pot, such as a Dutch oven. Add enough water to nearly cover the cabbage, along with the cinnamon stick, cloves, bay leaves, and salt and pepper.
Bring to a slow boil over medium high heat, then add the sugar and vinegar. Cover and reduce heat to medium low. Allow to simmer to for 30 minutes, until the cabbage is tender.
Add the apples and continue simmering until they are tender.
Remove the bay leaves and cinnamon stick. Taste for salt, vinegar, and sugar, adding more as needed.
Stir in the butter.
Create a slurry by mixing the cornstarch and water in a small bowl. Stir the slurry into the cabbage and allow to cook for another 2-3 minutes to thicken.