Slice the pork tenderloin at a long angle into 4 "steaks" and sprinkle with the thyme and a total of 1/2 teaspoon salt and 1/4 teaspoon pepper.
Heat the oil in a large skillet over medium-high heat until very hot, but not smoking. Add the steaks to the skillet and cook, turning once, until well browned and just a bit pink in the center, about 7 minutes per side. Turn the heat down to medium if the skillet starts to get too dark. Put each steak on a plate to rest.
While the steaks cook, core and slice the apple and thinly slice the cabbage. Stir together the broth, vinegar and sugar in a small bowl.
When the pork has finished cooking, add the cabbage, apples, 1/4 teaspoon salt and 1/4 teaspoon pepper to the same skillet. Cook, tossing, until slightly wilted, 2 to 3 minutes. Add the broth mixture and continue to cook until the cabbage is tender and the liquid has reduced slightly, 2 to 3 minutes. Remove from the heat and stir in the parsley leaves. Season with additional salt and pepper.
Divide the cabbage and apples and any juices in the skillet among the plates with the steaks. Serve with a roll.
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