NOTE: To make this quicker and easier you can use one 16-ounce bag of pre-shredded carrots and cabbage, called "Slaw Mix" instead of starting with whole cabbage and carrots. This dish can also be a one-pot-meal if you need to swap around. Just serve with some nice brown bread or whole-grain or whole-wheat bread.
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Heat 1 teaspoon of the oil in a large nonstick frying pan until hot but not smoking. Add the chops and brown on both sides, 1 to 2 minutes per side. Remove.
Carefully wipe out the pan. Heat the remaining teaspoon oil over moderate heat and add the onion, apples and remaining teaspoon fresh sage or 1/2 teaspoon dried. Cook, stirring occasionally, until the mixture is soft and golden brown, 4 to 5 minutes. Add the cabbage, carrots, vinegar and 1/2 teaspoon salt and continue cooking until the cabbage and carrots begin to soften, about 5 minutes. Add the broth and return the pork chops to the pan burying them in the vegetable mixture. Cover and cook just until the pork chops are just slightly blush in the center, 5 to 7 minutes longer.
To serve, arrange the warm slaw on individual plates and top with a pork chop and pan juices.