Rachael Ray has a sautéed red cabbage recipe that takes about 25 minutes, and the New York Times has a recipe for braised red cabbage with apples. This recipe lasts for about five days in the refrigerator.
To make the sautéed red cabbage, heat a skillet to medium high, add 2 tablespoons of extra-virgin olive oil and a small sliced onion, and sauté for about two minutes. Add half a shredded red cabbage, and turn it in the pan until it wilts, about three to five minutes. Add 1/3 cup of vinegar to the pan, and stir the cabbage into it. Sprinkle 2 rounded tablespoons of sugar over the cabbage, and mix it again. Season the cabbage with 1 teaspoon of mustard seed, salt and pepper, and then reduce the heat. Cook for about 10 minutes before serving, stirring occasionally.
To make the braised red cabbage with apples, cut a large red cabbage into thin strips and cover with cold water while preparing the other ingredients. Heat the oil in a large skillet over medium heat and add a thinly sliced small onion. Cook it for about three minutes, and add 2 tablespoons of balsamic vinegar before cooking for three more minutes. Add two cored, sliced tart apples, and cook for two to three minutes.
Drain the cabbage and add it to the pot, tossing to coat it, and then stir in 1/4 teaspoon of allspice, 2 tablespoons of balsamic vinegar and salt to taste. Stir, cover the pot, and cook for an hour, stirring occasionally before serving. Add salt, pepper or more vinegar to taste.