Heat oven to 400 degrees F. Lay a thyme sprig on either side of the pork tenderloin. Fold up tail end, using kitchen twine to truss every inch. Season with salt and pepper. Heat olive oil and butter in an ovenproof skillet over high heat. Sear the pork until brown, about 2 minutes per side. At the same time, brown apples, cut side down. Turn apples over; transfer skillet to oven, and roast until the internal temperature of the meat, when taken with a meat thermometer, is 145 degrees for medium and 150 degrees for medium well, about 10 minutes. Remove meat to a cutting board and let rest 10 minutes; reserve apples in a bowl. Return skillet to stovetop; deglaze skillet with apple cider, and reduce by half, about 2 minutes. Stir in vinegar, reduce 1 minute longer. Remove kitchen twine from tenderloins, and slice into 3/8-inch medallions. Place cabbage on platter, arrange pork medallions over cabbage, and top with apple halves and sauce. Garnish with thyme sprigs.;
Heat butter in medium skillet, over medium heat. Add cabbage, saute for 1 minute. Add caraway seeds and apple cider, and bring to a boil. Reduce to a simmer, and cook, stirring occasionally for 6 to 7 minutes. Add 1 tablespoon cider vinegar, and cook for 1 minute more. Remove from heat, and season with salt and pepper, to taste. Serve immediately.