My Granny made this red cabbage dish all my life. I love it, and started making it myself a few years ago. But I've changed a few things out of necessity (for example, Gran's recipe calls for cooking apples, which we don't get in Trinidad, so I just use the extra-tart granny smiths) and added a few things that I think add to the flavour of the dish.
You'll need a heavy cast iron pot to cook it in.
1 small red cabbage (sliced as thinly as you can manage)
2 granny smith apples (peeled and chopped into 1/2-inch pieces)
1 red onion sliced in thin circles
quarter cup of balsamic vinegar
3 tablespoons of cider or red-wine vinegar
quarter cup of maple syrup
1 bay leaf
3 cardamom pods
5 or 6 cracked allspice corns
2 star anise
1 cinnamon stick
salt and pepper (as you like it)
Put everything in the cast iron pot. Cover it tightly and let the ingredients cook gently on a very low heat for about 45 minutes. (The cabbage will spring its own juice.)